ELEMENTS OF PHYSi 



FISHER AND PATTERSON 






Class __Q_^L_^^ 



Copyiight]^"- 



COPYRIGHT DEPOSnV 



ELEMENTS OF PHYSICS 



EXPERIMENTAL AND 
DESCRIPTIVE 



BY 

AMOS T. FISHER, B.S. 

ASSISTED BY 

MELVIN J. PATTERSON, B.S. 



O «>t)0 Jj3 ->3 



>* > ** ^K"* J JOJJ^j'-* ^ ) ^ 



BOSTON, U.S.A. 



D. C. HEATH & CO., PUBLISHERS 
1902 



THE LIBRARY <»F 
Two Copies Receive* 

MAY. 5 1902 

.OOPVPI#MT CNTRV 

CLASS «-- XXa No. 
COPY B. 



Copyright, 1902, 
By D. C. Heath & Co. 



PRINTED IN 

UNITED STATES 

OF AMERICA 



Iplfmpton ipresfl 

U. M. PLiMPTON &. CO., PRINTERS & BINDERS, 
NORWOOD, MASS-, U-5^A. 



PREFACE. 

This book is the outgrowth of an attempt, covering a 
period of six years, to teach physics to young pupils in 
a manner which combines simplicity of language and 
presentation with the important manifestations of matter 
which constantly make up their environment. It is the 
aim of the text to combine experimental and descriptive 
instruction in order that both may be better understood. 

The authors have sought throughout this book to keep 
constantly before the pupils things and phenomena which 
they can see and observe. Plain, logical, and accurate 
statements of fact and explanations have been sought. 
Formulated statements of definitions and principles relat- 
ing to the subject have been brought out, and as far as 
practicable, the appHcation has been shown and illustrated. 
It has not been the intention to produce a complete work 
on any particular phase of the subject, but such an ele- 
mentary treatment of first principles as it is hoped will 
prove helpful and welcome. 

Most of the apparatus used in the work can be made at 
home, and will be a means of keeping interested many a 
boy who otherwise might not be. Such further apparatus 
as is needed may be secured at very moderate prices from 
Messrs. Alfred L. Robbins & Co., or Messrs. Walmsley, 
Fuller & Co., of Chicago, or the L. E. Knott Apparatus 
Co. of Boston and New York. 

A. T. F. 
M. ]. P. 



CONTENTS. 

CHAPTER PAGE 

I. Matter and Some of its Properties . . . i 

II. Motion and Force . 6 

III. Work and Energy 29 

IV. Mechanics of Fluids . 40 

V. Heat 55 

VI. Light 82 

VII. Magnetism 109 

VIII. Electro-Dynamics .116 

A- IX. Sound 157 

Index 181 



ELEMENTS OF PHYSICS. 



CHAPTER I. 

MATTER AND SOME OF ITS PROPERTIES. 

Matter. Definition. — Every object that has extension 
or that can affect our senses directly or indirectly is called 
matter. (This definition is only provisional.) Any ob- 
served condition or change in matter is a pJienomenon, 

Extension is that property or quality of matter by virtue 
of which it occupies space or takes up room. 

Questions. — What is an extended object ? Name some extended 
objects. How many of those named are material things ? How many 
can you perceive with one of the five senses ? Can you name some 
object which you can perceive with all of the five senses ? Can you 
name anything that can be perceived but is not material ? Describe 
some phenomenon. Is the sounc^ of a hammer a phenomenon ? Is 
a star a phenomenon ? Can you name some object not composed of 
matter ? How does one become aware of the existence of matter ? 
What reason have you for thinking that a tree w^hich you never saw is 
matter ? Why do you infer that the sun, moon, and stars are composed 
of matter ? Can you think of some sensation not due to matter ? 
Distinguish between matter and a substance. 

I 



2 Elements of Physics. 

CONSTITUTION OF MATTER. DIVISIBILITY. 

An experiment is an act or operation undertaken in 
order to verify some known or to discover some unknown 
principle or effect — a practical test. 

Experiment i. — Place a few crystals of sugar in your hand. Note 
their form, color, and taste. Then crush or grind some and examine as 
before ; place the powder under a microscope and examine. The crystals 
retain their original form, color, and taste. 

Experiment 2. — Put a teaspoonful of sugar into a half pint of water. 
Boil till the sugar dissolves. Let the liquid cool ; then taste a drop. 
Observe that the liquid is sweet. The sugar has been very finely 
divided and its particles have intermingled with the particles of the 
water. This forms a solution : the sugar is soluble in water, and water is a 
solvent of sugar. 

Pour half of the solution into another beaker and save it. To the 
remaining half add as much water. It is evident that the sugar has 
been much more finely divided in the last half than in the half set aside. 

If we should pour this solution into a gallon or barrel of water, what 
would be the result ? Would it affect the whole ? 

Limit of Divisibility. — The more we dilute the sugar 
solution, the finer we suppose its particles to be divided, 
since one portion tastes as sweet as any other, but the 
sweetness is less marked with each dilution. At this 
point a very interesting question arises : Would it be 
possible to go on dividing the sugar forever.'^ For ex- 
ample, if we should put a crystal of it into Lake Superior, 
would it continue to subdivide until every part of the lake 
contained a particle of sugar ? Experiments of this nature 
might lead one to suppose that there is no limit to the 
divisibility of matter. Other considerations, however, lead 



Matter and Some of its Properties. 3 

us to believe that there is such a Hmit, — that there is a 
smallest particle of sugar, or of any other kind of matter, 
which is incapable of further division except by such 
means as give rise to other forms of matter. These 
smallest particles are called molecules, 

A molecule is the smallest particle of a substance that 
can exist alone and have the same characteristics that a 
larger portion of the same substance has. 

In the above experiments we have performed what is 
known 'di'^ physical division, and we see that there are two 
ways by which such division may be accomplished: (i) by 
crushing or cutting, and (2) by solution. Although we 
may divide sugar or any other kind of matter into very 
minute portions by physical means, we may yet break it 
up into much finer parts by chemical means. By chemical 
action, however, new substances are formed having different 
properties or qualities, i.e. different form, color, taste, etc. 

Experiment 3. — Into the solution saved from Experiment 2 slowly 
pour sulphuric acid. Smoke arises, and the two clear liquids just united 
gradually turn black, and give off the odor of burning sugar. There is 
left a black substance resembling charcoal, and a liquid. 

The sulphuric acid has decomposed the sugar molecules into watei* 
and the black solid. 

An atom is the smallest particle of a substance that can 
exist, not alone, but with other atoms, to form molecules. 

Theory of the Constitution of Matter. — The theory of 
the constitution of matter generally adopted is that every 
body of matter is made up of very fine particles, called 
molecules, and that molecules are composed of still finer 
particles, called atoms. No two atoms of matter in the uni- 



4 Elements of Physics. 

verse are in permanent contact with each other, but have 
spaces between them probably larger than the atoms them- 
selves. 

DEFINITIONS. 

Volume is the amount of space that a body occupies. 

Mass is the quantity of matter that a body contains. 
It is independent of volume. A small lead ball may con- 
tain more matter than a large cork one. 

Density is the amount of matter that a body contains in 
a definite volume, or the mass or weight of its unit volume. 
E,g. if a piece of brimstone weighs 13 grams and has a 
volume of 6\ cubic centimeters, its density is 2 grams per 
cubic centimeter. 

Porosity is that property of matter by virtue of which 
spaces or pores exist among its molecules. Holes or 
cells like those found in sponges are, of course, not the 
kind of pores that are here meant. 

Elasticity is that property of matter which enables a 
body to resume its shape or size after it has been changed 
by some external force. All bodies have this property to 
some extent. Any body, when subjected to a pressure 
which does not exceed its elastic limit, will regain its 
original volume. upon the removal of the pressure. 

Liquids and gases have perfect elasticity of volume, but 
obviously have no tendency to regain their original shape 
after the removal of a deforming force. 

Some solids, such as lead and putty, have little power to 
regain their original shape after the action of a force upon 
them. Such solids are sometimes said to h^ plastic. 



Matter and Some of its Properties. 5 

Impenetrability is that property of matter which pre- 
vents any two bodies from occupying the same space at 
the same time. 

Experiment 4. — Fill a cup with water ; carefully drop into it a 
small piece of stone. The water rises in the cup and overflows, show- 
ing that water and stone do not occupy the same space at the same time. 

Indestructibility is that property of matter which pre- 
vents any particle of matter from being destroyed. 

Compressibility is that property of matter which per- 
mits substances to be forced to occupy a smaller space. 

Physics is that science which treats of the condition and 
properties of matter and such changes in it as do not 
destroy its identity. 



CHAPTER II. 

MOTION AND FORCE. 

Motion. — Every person has so clear an idea of motion 
that there would seem to be no difficulty in defining it 
absolutely. Yet we find that from remote ages men have 
been perplexed with its definition. For all practical pur- 
poses it is sufficient to define motion as, "A continuous 
change of position.'* 

Motion and rest, however, are only relative terms. 
When we speak of an object as being at rest, we mean 
simply that it is not moving along the surface upon which 
it stands. 

Suppose that you are standing still on a car which is 
moving slowly forward. This means that the car is con- 
tinuously moving, relatively to the ground, but that you 
are not changing your position in relation to the car. 
You see at once that relative to the ground you are in the 
same condition as the car, but that relative to the car you 
are at rest. Hence you are in motion or not in motion, 
according to the object to which you refer your position. 

If you should refer your motion to a car ahead of you 
which is going faster than your own, you would say that 
you were losing on that car ; i.e, relatively to that car, you 
would be going backward. 

6 



Motion and Force. 7 

Kinds of Motion. — When a body moves so that all points 
in it travel in the same direction and with the same velocity, 
the motion is said to be one of translation. Example : A 
train running on a straight track (if we disregard the earth's 
motions). 

A body moving to and fro in an oscillating manner is 
said to have vibratory motion. Example : The pendulum 
of a clock. 

A body of any size or shape made to turn upon an axis, 
or to spin around like a top, is said to have rotary motion. 
Example : A fly wheel turning on its axis. 

When the direction of motion continually changes, it is 
said to be curvilinear. Example : The moon revolving 
around the earth. 

Force. — When a person moves or brings his body to 
rest, he uses his will power and muscles. When a ball 
player puts the ball in motion or the catcher stops a ball, 
he exerts himself. If the batter hits the ball, he changes 
its motion. If the ball strikes the catcher's hand, even if 
he fails to stop it, he has exerted himself. In 
all the above cases we say that force was used 
to obtain the specified result. 



I 

/ 




\ 



Then, Force is that which tends to produce^ 
change^ or destroy motion. 

Experiment 5. — Suspend a pith 
ball by a fine silk thread as in Fig. i. 
With a catskin rub briskly a rubber rod . "'■' 

and hold it near the ball. What happens? Continue and observe all 
phenomena. Describe what you see. 



8 Elements of Physics. 

From this experiment we learn that there are two general 
kinds of force : — 

Attractive — which tends to bring portions of matter 
together, and, 

Repellent — which tends to keep portions of matter 
separated. 

Attractive Forces. — When we break a piece of iron or 
other substance, we overcome a force. When we heat 
two pieces of iron or glass until they become soft, and 
press them together, the molecules are brought into such 
close contact that they are held in the position in which 
we place them. This force which holds together mole- 
cules of the same kind is called cohesion. 

If we rub crayon over a blackboard or a lead pencil over 
some surface, a mark is made. That is, the crayon or pencil 
has parted with some of its particles, called molecules, and 
they stick to the surface rubbed. In these instances mole- 
cules of one kind are attracted by molecules of a different 
kind, and we call the attraction adhesion. Adhesion is 
manifested when water sticks to our hands, cust to our 
clothing, etc. 

Experiment 6. — Stretch a piece of sheet rubber very tightly all 
over the mouth of a jar. Pierce the rubber with the point of a knife 
blade. The hole instantly increases in size until it is much larger than 
the one which was cut at first. This indicates that the rubber was in a 
state of tension. 

Experiment 7. — Rub a sewing needle with a cloth until the needle 
is very dry. Then place it carefully on the surface of some water. If 
it is placed so that neither end touches the water first, the needle floats 



Motion and Force. 



in a sort of trough (see Fig. 2). The surface film of water is strong 
enough to hold up the needle, though the film bends under the weight. 

Experiment 8. — Place two pieces 
of a match on water and let a drop of 
alcohol fall between them. The two 
pieces instantly separate. Fig. 2. 

These experiments suggest that water is covered with a 
film, in a state of tension, which the alcohol breaks. As 
the knife blade pierced the rubber, so the alcohol pierced 
the film on the water, and this hole increased in size just 
as the hole in the rubber did, causing the pieces of match 
to separate. 

Experiment 9. — If a piece of glass is inserted in water, the surface 
film will not be broken, but instead of springing away it will rise up on 

the sides of the glass (Fig. 3). This is be- 
cause the adhesion between the glass and 
water is stronger than the cohesion between 
the molecules of water, and stranger than 
the elasticity of the film. 

Experiment 10. — If a glass is inserted in 
mercury, the surface film will not be broken, 
but will be pushed down as a cloth which lies on the surface of water 
may be pushed down by a stick, and the surface of the liquid next to 
the glass will be convex (Fig. 4). This is 
evident from the fact that bits of paper 
dropped on the surface of the mercury are 
pulled toward the glass and downward as 
the glass is pushed into the mercury. This 
indentation of the mercury by glass is due 
to the fact that the cohesion between the 
molecules of the liquid is stronger than the adhesion between the liquid 



Fig. 3. 





f 




/" "N 


r > 



Fig. 4. 



lO 



Elements of Physics. 



and the glass. Whenever such conditions exist, the liquid will not wet 
the soHd. 

If a tube is used instead of a flat piece of glass, the result will be as 

shown in Fig. 5, and the smaller the 
tube, the greater the interior elevation 
or depression. 

This elevation or depression 
of a liquid is called capillary 
action, because best seen in fine 
tubes {capillus^ a hair). 





Water 



Mercury 



Fig. 5. 



Upon the cohesion of the 
molecules of soUds several other 
properties of solids depend, the most important of which 
are ha^^dness, tenacity, ductility, and malleability. 

Hardness is that property of solids which enables them 
to resist being scratched. The diamond is the hardest 
known substance. It will scratch every other solid. 

Tenacity is the property of solids which enables them 
to resist being pulled in two. Steel is one of the most ten- 
acious substances. A steel pianoforte wire ^^ of an inch 
in diameter will sustain the weight of a very heavy man. 



Ductility is that property of solids which enables them 
to be drawn into wire. Platinum is the most ductile of 
metals. It can be drawn into wire so fine that it can be 
seen only through a microscope. 

Malleability is that property of solids which enables them 
to be hammered or rolled into sheets. Gold is the most 
malleable of metals. It may be rolled into sheets so thin 



Motion and Force. 



II 



that they cannot be seen edgewise without the aid of a 
microscope. 

When two parts of a solid or of two different soHds are 
brought into such close contact after heating that cohesion 



Water 



Fig. 6. 



Mercury 



is made effective, the process is called welding. Example : 
The mending of broken iron or brass rods. 

Laws of Motion and their Application. — Momentum is 
the quantity of motion belonging to a moving body. It 
is the product of the mass of the body multiplied by its 
velocity. For example, if a body weighing 50 pounds 
is moving at the rate of 20 feet a second, its momentum 
is 50 X 20, or 1000. If a change is required in the momen- 
tum of a body, a change in its velocity is necessary; e.g. if in 
the example given above, 2000 is the required momentum, 
the velocity must be changed to 40 feet per second ; or, 
if momentum is to be changed without a change in velocity, 
the mass must be changed. 

The effect of force in producing a change in the con- 
dition of rest or motion of bodies is fully explained and 
described by the following propositions known as Newton s 
Laws of Motion : — 



I 2 Elements of Physics. 

I. A body at rest remains at rest, and a body in motion 
moves with tiniform velocity in a straight Itne^ unless acted 
upon by some external force. 

II. Change of m^omenttim is in the direction in which the 
force acts, and is proportional to its intensity and the tim.e 
during which it acts. 

III. To every action there is an equal and opposite 
reaction. 

Discussion of First Law. — Any body at rest, then, has 
perpetual rest, or in motion has perpetual motion, if no 
force interferes. This property of matter on account of 
which it is incapable of changing its condition of rest or 
motion is called iriertia. 

Discussion of Second Law. — Stating this law as Newton 
stated it, we have : The change of motion is proportional to 
the impressed moving force, and takes place along the right 
line in which that force is impressed. 

If a force generates a certain momentum, double that 
force will generate double that momentum, and treble 
that force, treble diat momentum, etc. This will be the 
case whether the forces have been impressed simul- 
taneously, at a single instant, as when a body is struck 
a violent blow ; or gradually and successively, as when 
the forces continue to act on a body for a definite length 
of time. 

This second law affords a means of defining and measur- 
ing forces. According to this law, the changes of momen- 
tum which a number of forces separately produce in a 
given time are proportional to the forces. If, therefore, 



Motion and Force. 13 

the forces all act in succession on the same mass, the 
changes in velocity will be in proportion to the forces. 
Thus we may measure the relative magnitudes of the 
forces by finding the change in velocity which each force 
produces in a given mass in a given time. 

Discussion of Third Law. — When we deal with the 
effect of a force upon a body with which we happen to be 
concerned regardless of any other body, we speak of this 
effect as action. For instance, if a sledge is used to drive 
a post, we speak of the action of the sledge hammer upon 
the post. If we consider the effect of the force of the 
post upon the sledge, we speak of it as reaction. When- 
ever there is a force applied there must be action and 
reaction. 

Mass Attraction : Gravitation. — The fall of the leaves, of 
the rain, in fact of all bodies when they have no support, 
teaches us that there is an attraction between them and 
the earth; and it has been proved that the attraction is 
mutual. In 1798 Cavendish proved by a series of 
experiments that two balls mutually attract each other, 
and that any two bodies have an attraction for each 
other similar to that which the earth exhibits toward 
them. Cavendish's experiment has been repeated by 
several observers since his time with the same general 
result that he obtained. 

Sir Isaac Newton was the first to announce that such 
mutual attraction exists between the earth and the moon, 
and the sun and the stars. There is mutual attraction 
between all bodies, whatever their sizes or distances. 
This attraction is called gravitation. 



14 Elements of Physics. 

Newton's law of universal gravitation states that ''the 
attraction betzveen any two bodies vaides as tJie product of 
tlieir masses and inversely as tlie square of the distance 
betzveen their centers of ^nass^ 

For instance, if two bodies, A and B, weigh loo pounds 
and 25 pounds respectively, it is evident that the attraction 
which A has for a third body, C, is four times that which 
B has for C, at the same distance from it. Now suppose 
that A and B are a foot apart and we designate the power 
of attraction operating between the two bodies by i. If 
we place them two feet apart, their attraction will be desig- 
nated by ^ ; at three feet apart by \, etc., according to the 
last part of the law. 

When reference is made to the attraction which the 
earth has for bodies near it, the term gravity is used, 
though there is no real difference between gravity and 
gravitation — both act according to the same law. Hence 
the weights of different bodies at the same place vary as 
their masses. This principle enables us to compare the 
quantities of matter in two bodies by means of a beam 
balance. We must not lose sight of the fact, however, 
that a ponnd is a quantity of matter^ while the zveight of 
a ponnd is a quantity of force. 

Gravity is everywhere puUing bodies toward the center 
of the earth. Bodies free to fall take a direct line toward 
that point, and this line is called their line of diirction. 
Are all Hues of direction parallel } FalUng bodies are 
directed downward in every country. What does down- 
ward mean } 



Motion and Force. 15 

Gravity never for an instant ceases. It is a constant 
force, and on the same mass at the same place its amount 
is always the same ; hence gravity not only starts a body 
falling, but gives it approximately the same increase in 
velocity for every second of its fall. Why say approxi- 
mately ? Motion in which the velocity changes as much 
in each succeeding unit of time as it does in the first is 
called tcniformly accelerated motion. The motion of a fall- 
ing body would furnish a perfect example of this if it were 
not for (i) the resistance of the air, which is very great on 
swiftly moving bodies, and (2) the slight increase in the 
force of gravity as the body approaches the earth. 

Galileo proved that the acceleration due to gravity is the 
same for all bodies; i.e. that wax balls, iron balls, and paper 
balls fall at the same rate when free from the action of the 
atmosphere. This is shown by placing bits of paper, wax, 
iron, shot, etc., in a long tube, and, after exhausting the 
air, turning the tube end for end so that the bits may fall. 

Experiment ii. — Take a large grooved wheel A (Fig. 7) that turns 
very easily on its axis, and fasten it to the ceiling ; then take a long 
strip of board B marked in feet, and place it as in the figure, and attach 
to it the movable ring E. and a small platform C arranged to drop at 
the first swing of the pendulum B. Over the wheel A place a light 
cord with two weights M and TV, having exactly the same mass ; 
neither moves. Raise the weight A", and let it rest upon the plat- 
form C\ then place the weight J\f, called a rider, on N. When the 
pendulum D is set in motion the platform C falls, and A^and X com- 
bined, being heavier than M^ move downward. By repeated trials it 
is found that N and X move two spaces during the first stroke of the 
pendulum. Now add in place of X the weight P", twice as heavy as X^ 
and it will be found that N and Y will go nearly twice as far as N and 



i6 



Elements of Physics. 



X did during the same time 

] 




lO 



12 



m 



X 



6 gr. 



Here the force is doubled and the dis- 
tance nearly doubled, consequently 
the velocity and the momentum 
generated are nearly doubled. Had 
the masses moved in both cases 
been the same, the velocity and 
momentum would have been exactly 
doubled, but when the weight X is 
used, a force of 6 grams puts M and 
A^ and X, or 242 + 242 + 6 grams 
= 490 grams, in motion ; while V 
puts 242 + 242 + 12 grams = 496 
'Eiders, grams in motion. 

These results show that m 
equal intervals of time change 
of momenttifn is prop07'tional 
to the force applied. 



12 QT. 



Jfovahle Bing. 



M 



Fig. 7. 



Place X on JV, and by repeated 
trials it will be found that in two 
units of time they will move nearly 
four times as far as in one unit of 
time, and in three units of time 
nearly nine times as far. 

This result shows that the 
mojnenttim generated by a 
given force is proportio7ial to 
the time dtiring which the 
force acts. 

Further, it will be found by put- 
ting the ring^ at 2, and the weights 



Motion and Force. 17 

iVand X on the platform as at first, that the weights will move to 2 in 
one unit of time. At 2 the weight X will be caught off, and the weight 
N (under the momentum generated by X from i to 2) will proceed to 4 
in conformity with the first law of motion. By leaving ^ on A^it will 
be found that they go one space farther than above, i.e. they would 
move through four spaces in two units of time. Continuing, it will be 
found that by catching X off at 5, N will proceed to 9 in conformity 
with the first law of motion. The weights have at the end of the 
first unit of time a velocity of two spaces, and at the end of the second 
unit of time a velocity of four spaces. But they started from rest, hence 
the constant force causes during the first unit of time a gain in velocity 
of two spaces per unit of time, and during the second unit of time an 
additional gain in velocity of two spaces per unit of time. 

Therefore, the ejfect of a constant force is to produce uni- 
formly accelerated motion. 

The velocity of a body at a given instant is the rate of its 
motion in a definite direction at that instant ; if the direc- 
tion is not expressed, the rate of motion is called speed. 

If motion is uniform, the velocity is constant, and is 
expressed by stating the distance moved over in a unit of 
time, as 10 miles an hour, 20 feet a second, and so on. 
As the spaces gone over are equal for equal units of time, 
it follows that for two such units of time the distance would 
be twice as great ; for three units of time it would be three 
times as great, and so on; i.e. the distance gone over by 
any moving body is proportional to the time. 

If a body moves with a uniform velocity of 80 miles an 
hour, in 10 hours it will travel 800 miles. Now if v 
represents the velocity, t the time during which it moves, 
and s the space traveled, we see that the whole distance 



1 8 Elements of Physics. 

traversed equals the product of the velocity and the time, 
i.e. s = vt. From this it follows that for uniform motion 

the velocity for a unit of time equals the space gone over 

s 
in a given time divided by that time, i.e. z; = -, and that 

the time required to traverse a given space with a given 

s 
velocity equals that space divided by that velocity : t = -. 

V 

It is very important to remember that if the velocity 
changes in the least, acceleration or retardation must 
have occurred during the change ; or if a body has been 
set in motion from a state of rest, its motion has been 
accelerated^ and that if its motion increases or decreases by 
equal amounts in equal times, it is 2mifor7nly accelerated or 
retarded. 

Laws of Uniformly Accelerated Motion. — Let a denote 
the change in velocity per second; that is, the acceleration. 
Then if a body starts from rest, its velocity in one second 
will be a units, at the end of two seconds 2a units, etc.; 
and in / seconds it will be / X ^ units or at units, i.e. v = at] 
stated thus, the velocity at the end of time, t, due to accelera- 
tion, equals tlie product of the time a7id the rate of accelera- 
tion. For example, a train starts from a station and runs 
for 6 hours at a regularly increasing rate of speed. Its 
velocity at the end of the first hour is lo miles per hour, at 
the end of the second hour 20 miles per hour, at the end 
of the third hour 30 miles per hour, etc. During the entire 
6 hours it will gain a velocity of 6 x 10 = 60 miles per 
hour, i.e. 60 = at. 

Experiment has shown that a falling body has an ac- 
celeration of approximately 12\ feet per second (in a 



i 



Motion and Force. 19 

vacuum); then its velocity at the end of four seconds 
would be 4 X 32^ or I28| feet per second. 

In the case of a freely falling body which starts from 

rest and falls for t seconds, the velocity at the start is 

o feet per second, and it increases at a uniform rate until 

at the end of / seconds it is <^ x ^ feet per second ; hence 

r 1 11 . , + a y. t 
the average velocity for the whole time is — or 

— feet per second. If s represents the distance traveled 

T . , . . , at afl , ^9 

during^ the entire time /, we have s = — x t or — or^ ar. 

The law is stated thus : The space traveled by a body 
tender miiformly accele7'ated motio7i in a given time equals 
one half the product of the acceleration and tlie square of tlie 
time. For instance, a ball is thrown vertically upward and 
strikes the ground in 8 seconds. How high did it go } 
The ball would take just as long to go up as to return, 
hence it falls in 4 seconds. Then by substitution, s — 
\ at'^ becomes s = ^ x 32^ x (4)^, or i- = 257^ feet, the 
height to which the ball went. 

Now taking the two equations, v = at and s = \at'^y and 
combining them algebraically: 

(i) v = at. (2) s^^at'^. 

From (i) t = -, and /2 = -^, 

a a^ 

from (2) t^ = — , then by axiom ^ = — ; 



from which s = — , and v = V2 as. 

2 a 



20 Elements of Physics. 

Problems. — I. A body falls from rest: find the distance traversed 
in feet and the velocity acquired : {a) in 5 seconds, {b) in | a minute, 
(c) in 15 minutes. 

2. A body falls freely from rest. In what time does it travel 300 
yards ? What is its final velocity ? 

3. A falling body acquired a velocity of 224 feet per second. How 
far did it fall? 

4. A body falls from rest 400 feet. Find its velocity when it strikes 
the ground, and the time it takes to fall. 

5. A ball was thrown upward and struck the ground 9 seconds after- 
ward. How high did it go? With what velocity did it start? How 
far below its highest point was it 5 seconds after it started? 

6. With what velocity must a stone be thrown upward that it may 
rise 121 feet? 

7. A stone is thrown upward with a velocity of 160 feet per second. 
How high will it go? How long will it be in the air? 

8. A body is thrown from the bottom of a well Sa feet deep with a 
velocity of 5 <^ feet per second. Find the time required for the body to 
fall from its highest point to the surface of the earth? 

9. A body falls freely from rest. How far will it travel during the 
first 2 J seconds? How far during the third half second? 

Composition and Resolution of Forces and Motion. — 

Everyday experience indicates that the effect which two 
forces have when acting together upon a body may be pro- 
duced by a single force; that is, a single force can be found 
which will produce the same effect on a body which the 
two forces produce when acting together. This one force 
is called the resitltaiit of the forces to which it is equivalent, 
and the two forces are called the components of the resultant. 



Motion and Force. 21 

A force which will exactly neutralize or balance a combi- 
nation of two forces is called the eqiiilibrant of those forces. 

The resultant of two forces which act from the same 
point and in the same direction is found by taking the sum 
of the forces. For example, if two forces of 4 and 5 lbs. 
respectively, act from the same point and in the same 
direction, the resultant of the forces is 4 + 5 = 9 lbs. 

The resaltant of two forces which act from the same 
point and in opposite directions is found by taking the 
difference of the forces. For example, if two forces of 4 
and 5 lbs. respectively, act from the same point and in 
opposite directions, the resultant of the forces is 5 — 4=1 lb. 

When two forces act from the same point, but in di- 
rections which make an angle with each other, the magni- 
tude of the resultant depends upon the size of the angle. 
For example, if two forces of 3 and 4 lbs. respectively, act 
from the same point and in directions which make an 
angle of 90° with each other, the resultant of the forces is 
V32 + 42 = 5 lbs. Let AC^Xid^AB c n 

be forces of 3 and 4 lbs. respectively, 
acting from the point A. Let the 
angle BA C be an angle of 90°. AR 
is the diagonal of the parallelogram 
ABRC 2in.^ represents the resultant 
of the two forces. ^ ' fig 8 



By geometry AR =^AC^ + AB^. 

If the angle included between the lines of direction of 
two forces be other than a right angle, the resultant can 
still be found by the principles of geometry or trigonom- 
etry. When the angle between the forces is 30"^, 45°, 60°, 



2 2 Elements of Physics. 

or 120°, it is possible to solve by geometry or trigonometry; 
for other angles trigonometry must be employed. 

The value of the resulting momentum produced by a 
force will vary according to the following conditions : — 

(i) If a force acts upon a body which is already in mo- 
tion, the momentum produced (which must be in the di- 
rection in which the force acts) must be added to that which 
the body already has if both are in the same direction, or 

(2) subtracted from it if they are in opposite directions. 

(3) If the force is in a direction inclined at an angle to the 
direction of motion of the body, the forces are compounded 
to obtain the resultant. 

Example of the ist. — If a body of 40-ton weight is moving 20 feet 
per second, it has a momentum of 800 ; but if it is struck by another 
body of 40-ton weight moving in the same direction at 30 feet per 
second, the resuhing momentum is the sum of 800 and 1200, or 2000. 

Example of the 2d. — If the latter body moves in the opposite direc- 
tion, the resulting momentum is the difference between 1200 and 800, 
or 400, and tends to produce motion in the direction of the larger force. 

Example of the jd. — If the latter body moves at an angle to the 
direction of the former, the resulting momentum will be neither the sum 
nor the difference, but will be a combination of the components, depend- 
ing upon the size of the angle. If the angle is a right angle, the resulting 
momentum will be the square root of (800)^ + (1200)2, qj- 1442 + . 

From these statements we infer that any force produces 
the same change of momentum whether it acts alone or 
with some other force, and whether the body acted upon is 
in motion or at rest. 

Experiment 12. — Place a piece of cardboard so that one end pro- 
jects over the edge of the table. On this balance two small wooden 



Motion and Force. 



23 



balls of equal size and weight, B and C (Fig. 8). Strike B (the one 
over the table) with the spring vi so that it will be projected toward E. 
C acted upon by gravity falls directly to D. But B is also acted upon 
by gravity and instead of going to E it falls with a curvilinear motion 
to F'm the same time that C is falling to D, 




Fig. 9. 



Thus we see that gravitation had the same effect on B 
that it had on C, although another force was acting on B 
at the same time. This experiment also shows that a force 
produces the same effect whether the body acted upon is 
in motion or at rest. 

Problems. — I. If two forces of 30 and 40 lbs. act upon a body at 
right angles to each other, what will be the value of the resultant 1 

2. Two forces acting upon a certain body are capable of producing 
velocities of 25 and 50 feet per second respectively. What velocity 
would both produce if they acted at right angles at the same time? 

3- Two forces of 12 and 15 lbs. act upon a body in lines which meet 
in a point and are at right angles. Find the magnitude of the resultant. 

4. Two horses are pulling on a stone with forces of 2000 lbs. each ; 
one pulls toward the north, the other toward the east. What is the 
magnitude of the resultant of their pulls ? 



24 Elements of Physics. 

Center of Mass or Gravity. — Every particle of a body is 
acted upon by the force of gravity ; i.e, the earth exerts a 
force or pull upon each of the body's particles, and these 
pulls, acting toward the center of the earth, constitute 
what is practically a set of parallel forces. The total 
effect of gravity, then, upon a body is the resultant of 
these parallel forces. 

The point of application of this resultant, and hence the 
point of application of its equilibrant, or balancing force, is 
called the center of mass or center of gravity of the body. 

Equilibrium. — Manifestly we may find the center of 
gravity of a body by finding the point upon which it will 
balance, i.e. the point at which a single upward force will 
balance or equilibrate all the earth's downward pulls upon 
the body. When a body is thus balanced, it is said to be 
in equilibrium. 

Any body is in equilibrium if the resultant of all the 
forces acting upon it is zero. 

Bodies may be in either (i) stable, (2) unstable, or (3) 
neutral equilibrium. 

1. If a body when tipped or tilted through a small angle 
tends to right itself, or, in other words, if the force tending 
to overturn the body has to raise its center of gravity, the 
body is in stable equilibrium (Fig. ic\ 

2. If a body when slightly tilted tends to overturn, i.e. 
the tilting force lowers the center of gravity, the body is in 
unstable equilibrium (Fig. 11). 

3. If the tilting force tends neither to raise nor lower 
the center of gravity, the body remaining indifferently wher- 
ever placed, the body is in neutral equilibrium (Fig. 12). 



Motion and Force. 



25 



When we speak of the stability of a body, we usually 
refer to the size of the angle through which the body must 
be tipped to overturn it. This depends upon the area of 
the base on which the body rests and the height of the 
center of gravity above the base. For instance, a body 
having a base 3x4 feet and a height of 2 feet is more 





Stable 
Fig. 10. 



Unstable 
Fig. 11. 




Neutral 
Fig. 12. 



stable than a body having the same base and a height of 
10 feet. Again, a body 10 feet high having a base 6x8 
feet is more stable than one of the same height with a base 
3x4 feet. 

Questions. — i. In what kind of equilibrium is a house? A wagon? 
A barrel when on its side? A person when standing? A coin when on 
its edge? 

2. Which is more stable, a load of hay or a load of rock? Why? 

3. Compare the stability of a pyramid with a cube having same 
base and altitude. 

4. Why do we lean forward when climbing a hill? 

5. Why do quadrupeds learn to walk so much earlier than children? 

6. Why do we turn the front wheel of a bicycle so frequently when 
learning to ride ? 

Pendulum. — Any body suspended so that it is free to 
swing may be called dipenduhtm. The most common form 



26 Elements of Physics. 

consists of a heavy metallic weight, called the bob, sus- 
pended by a slender rod or wire which is very thin and 
flexible at the top. The swing of a pendulum from one 
end of the arc to the other is called a vibration ; and half 
the arc through which it swings is called the amplitiide of 
vibration. 

Experiment 13. — Suspend an iron ball by a cord one meter long, 
set the ball to swinging, and time it carefully ; you will find that it will 
vibrate approximately sixty times per minute whether it swings through 
a long or a short arc. The tiuie of vibration is practically ijidepeiident of 
the amplitude. Next make the length of the cord which supports the 
iron ball \ meter, set the ball to swinging, and time as before. You will 
find that it vibrates twice as many times per minute as in the first trial. 

This experiment shows that the shorter the pendulum, 
the quicker the vibration, and that the time of vibration 
vajies directly as tJie square root of tJie length. 

Experiment 14. — Place a strong magnet under the ball very close 
to it, and note that the pendulum gains several vibrations in swinging 
for three minutes, showing that the attraction of the magnet lessens 
the time of vibration. 

By experiments too difficult for an ordinary laboratory it 
has been ascertained that gravity produces a like result and 
that the time of vibratio7i of a penduhtm varies inversely as 
the square root of tJie i7itensity of gravity. 

Experiment 15. — Suspend several pendulums of the same length, 
but of diiferent material and weight, and note that they swing at the 
same rate, showing that the time of vibration is independejit of the 
7naterial or weight of the bob. 

Curvilinear Motion. — Motion is said to be curvilinear 
when its direction continually changes. 



{ 



Motion and Force. 27 

We learn from Newton's first law of motion that every 
moving body travels always in the same direction — i.e. in 
a straight line — unless compelled to depart from it by 
some external force ; therefore force is necessary to change 
the direction of a moving body. 

It is evident, then, that curvilinear motion can be pro- 
duced in a body only by a force acting continuously upon 
the body at an angle to the straight line in which the body 
tends to go, so as to constantly change its direction. When 
a body moves in a circle, this force acts at right angles 
to the direction in which the body moves, i.e. toward the 
center of the circle. 

Centripetal Force. — This deflecting force is, then, 
properly called the central or centiipetal force. 

If the centripetal force be stopped from acting upon a 
body which is traveling in a circular path, the body con- 
tinues to move in a straight line tangent to the circle at 
the point where the body was when the centripetal force 
ceased to act. 

Hence it may be said that a revolving body tends to fly 
away from the center tange7itially, and a centripetal force 
is necessary to keep it in its circular path. . 

Experiment i6. — Cause a ball to revolve about the hand by means 
of a string attached to it and held in the hand. Your hand imme- 
diately begins to pull on the string to prevent the ball from flying off. 
By continuous exertion the ball is made to fly in a circle with great 
speed. The momentum produced in the ball by the motion of the 
hand in starting it acts at right angles to the string and represents the 
tangential force. By suspending the ball and striking it at right angles 
to the string, the same curvilinear motion is produced. 



2 8 Elements of Physics. 

Centrifugal Force. — The pull which one feels upon the 
hand when rapidly revolving the ball in Experiment i6 is 
really the reaction of the revolving ball upon the force 
exerted in deflecting the ball from a straight line path. 

This reaction is called centrifugal force. 

Questions. — i. Is there any possibility of the earth ever wandering 
from its orbit? Why? 

2. Explain the principle of revolving clothes dryers used in laundries 
and of cream separators. Name other machines acting under the same 
principles. 

3. Why do circus horses and riders lean toward the center of the 
ring? 

4. Why is the outer rail on railroad curves higher than the inner 
one? 

5. Why is it not safe to turn a grindstone very rapidly? 

6. Why has the earth its present shape? 

7. What influence has centrifugal and centripetal forces upon tides 
and winds ? 



CHAPTER III. 

WORK AND ENERGY. 

Work. — - If a man lifts a stone and moves it from one 
place to another, we say that he does work — causes mo- 
tion in the stone. If he should carry the stone to the top 
of a steep hill, he would do work, and if the stone should 
roll back again, gravitation would move it as far as the man 
did ; hence would do as much work as he did. Whenever 
any force moves a body it is said to do work. We see, 
then, that force and distance are essential elements of work. 
A man may support a stone until he becomes weary, yet he 
does not do work, because he produces no motion. If he 
exerts greater force and the stone rises, he does work upon 
it, but if he lessens his force and the stone presses him 
downward, work is done upon him by the stone. A body 
that moves another does ivork tipon it, ajid the body moved 
has woi'k done tipon it. 

Work may be defined as the doing of something against 
opposition, or the overcoming of opposition. 

Energy. — When we speak of a person having much 
energy, we mean that he can do much work. By this we 
may mean bodily work or mental work, or both, but in 
physics we mean only his muscular ability to do work. 
When we say that some inanimate body has energy, we 
mean that it possesses the ability or power to do physical 
work. Energy, then, may be defined as the capacity for 

29 



30 Elements of Physics. 

doing work. It is measured by the quantity of work the 
body possessing it can do. Hence the units of work and 
energy are the same. 

The act of doing work consists in the transfer of energy 
from one body to another, or in the transformation of one 
kind of energy into another ; as when a hammer strikes 
a nail and drives it into a board, the energy of the hammer 
is transferred to the nail, or if the nail lies upon an anvil, 
the energy of the hammer is transferred into heat. 

Work^ then, may be defined as the act of transferring or 
transforming energy. 

Kinetic Energy. — Experience teaches us that a body in 
motion can impart motion and can do work upon another 
body ; i.e. it possesses energy. This energy due to a 
body's motion is called ki^ietic eiiergy. 

Potential Energy. — The energy which a body has be- 
cause of some attraction or repulsion between its parts, or 
between it and other bodies, is called potential energy. If 
a stone is thrown upward, it has kinetic energy as it rises ; 
but at a certain point its motion becomes zero, and its 
kinetic energy ceases for the time ; it is not lost, but is 
changed into potential energy and is regained as the body 
falls. The energy the body gains while rising is stored up 
by virtue of its elevated position, and at the point where its 
motion is zero the body may be said to have a position of 
advantage with reference to its surroundings and hence to 
possess potential energy. Potential energy implies force or 
a tendency to motion as truly as kinetic energy implies 
motion. 

A stone lying on the ground possesses no energy, for it 
is powerless to do work because it lies where it cannot 



Work and Energy. 31 

move. Place the same stone upon a shelf. In raising the 
stone you do work on it. It now seems as devoid of energy 
as when on the ground. Attach one end to a smaller stone. 
Pass the cord over a pulley and remove the supporting 
shelf. The larger stone, because of the attraction be- 
tween it and the earth, falls, and in so doing raises the 
smaller stone, thus doing work. 

The larger stone is able to do work in falling because 
of the potential energy which it possesses when on the 
shelf. 

Energy, then, may exist in bodies actually moving or in 
bodies having only an opportunity to move. That a body 
may possess energy it must have some force, called a 
stress, acting upon it, and have actual motion or advan- 
tage of position. 

Questions. — What kind of energy has a bent bow? A coiled spring? 
A moving train? A charge of gunpowder ? A running horse? 

Practical Units of Work and Energy. — The unit adopted 
for work and energy is the amount of work done in raising 
a one-pound mass one foot. It is called the foot-pound. 
A unit of work in the metric system is the work done in 
raising a gram mass one centimeter. This unit is called 
the grmn-centimeter. The work done in raising a kilogram 
mass one meter is also sometimes used as a unit of work. 
It is called the kilogram-meter. 

There are many kinds of work besides raising weights ; 
but when the resistance is the same, the work in any other 
direction is the same as in the vertical. Hence it is easy 
to calculate the work when the resistance and distance are 
known. 



32 Elements of Physics. 

Problems. — i. It took a force of lo lbs. to pull a saw across a 
piece of wood, and loo strokes of 2 feet each to saw the wood in two. 
What amount of work was done? 

2. Compare this with the amount of work done by a bullet in pene- 
trating a plank 4 inches against a resistance of 800 lbs. 

3. How much work is done in winding a clock whose weight of 40 
ounces is raised 42 inches? 

4. How much work would you perform in climbing the Washington 
monument? (Height, 555 feet.) 

5. How much work is done in coming upstairs, there being 50 steps 
of 8 inches each? 

6. Where is the energy that was expended in raising the stones to 
their places in building the Egyptian pyramids ? 

Formulas for Calculating Energy. — It has been proved 

that s= — (accelerated motion). 

2 a 

But F=Mxa, (i) 

and E or W= Fx s ; (2) 

then E or W= Afx a x s, 

and E or IV= M x ax 

2a 

Hence E or W^ — • (3) 

2 

F=^ M xa, then M= -• 

a 

But in falling bodies F= Wt, then 7J/=— • 

a 



Work and Energy. 33 

Putting- for M in (3), we have 

E or W= (4) 

^. _ 2 ^ 

Machines. — A machine is a body or combination of 
bodies so arranged that force and motion may be trans- 
mitted and modified. 

Levers. — A lever is an inflexible pivoted bar by which 
xorce at one point may balance a fores at some other 
point. Any appliance which is equivalent to such a bar is 
a lever, no matter what its form. The working force is 
called the power ; the force worked against is called the 
weight ; the pivot upon which the lever works is called the 
fulcricm. The perpendicular distance from the fulcrum to 
the line of direction in which the power acts is called the 
pozver-arm ; the perpendicular distance from the fulcrum 
to the line of action of the weight is called the weight- 
arm ; the distance through which the power moves is 
sometimes called the power-distance, and the distance 
through which the weight moves is called the weight- 
distance. 

Experiment 17. — Arrange a large weight, a lever, and a fulcrum as 
in Fig. 13, with the fulcrum F 3 

inches from the weight IV. At a ^^s=:==^?^^BSl ..'<^^^^^^^\ 

point 57 inches beyond F^ place 
a weight, P^ which will balance 
or raise W. But in raising W 
\ inch, P was lowered 9J inches, 
showing that the power: arm {Pa) 

bears the same ratio to the weight-arm {Wa) that the power-distance 
(/W) bears to the weight-distance ( Wd) . 




34 



Elements of Physics. 



Experiment i8. — Balance a bar as in Fig. 14, place a weight IV of 
2 ounces at 12 inches from /^, and find that a power, P^ of i ounce at 24 

F 



I I I I I QJ 



^" 



I '''■'''■' I ■ ' ' ' ' 



Fig. 14. 



inches from F exactly balances it. Then try 5 ounces at 5 inches, and 
I ounce at 25 inches from /^ ; 6 ounces at 5 inches, and i ounce at 30 
inches ; and 467.5 grams at 4 inches, with 85 grams at 22 inches » 

These trials show that the weight bears the same ratio 
to the power that the power-arm bears to the weight-arm, 
and that the power-distance bears to 
the weight-distance ; z.e. 

W:P::Pa: Wa::Pd: Wd. 

These experiments also prove that 
the work done by the power and 
weight are equal. 

Experiment 19. — Arrange a wheel and axle, 
as in Fig. 15, the diameter of the wheel being 
three times that of the axle. Wind a cord 
around the wheel and another in the opposite 
direction around the axle. Suspend a weight of 6 lbs. from the 
axle and another of 2 lbs. from the wheel. These two weights 
balance, showing that W \ P \\Pa\ Wa. A careful study of the ex- 
periment also shows that W \ F^\ : Pd : Wd. 

Levers are divided into three classes, as in Figs. 16, 17, 
and 18. State in words the conditions existing in each 
class. 

In each class of lever it is true that P : W:: Wa : Pa. 




Work and Energy. 



35 



Experiment 20. — Suspend a single pulley as in Fig. 19. Then 
take a string with two equal weights of 30 lbs. each attached to the 
ends, and place it over 
the pulley. The two 
weights balance each 
other. Move one, called 
the power, dow^nward, 
wdiile the other, the 
weight, will go upward, 
both moving the same 
distance. In this case 
P -.W '.:Wd :Pd. 

Experiment 21. — 
Suspend a fixed ^^ulley 
A and a light movable /3^ 
one B so that there 
will be equilibrium, Fig. 
20. Suspend from B a 
weight W of 105 units, and on the other side of A fasten a single ball 
weighing 52 J units. The single ball supports a weight twice its own. 




Fig. IV. — A Lever of the Second Class. 



P 



Fig. 18.— a Lever of the Third Class, 




130 

Fig. 19. 




36 



Elements of Physics. 



Thus by the use of this machine a power is able to balance a weight 
twice as great as itself. Upon lifting the weight we find that the power 
moves through twice as much distance as the weight, thus showing 
P\W::Wd:Pd. 

Experiment 22. — Arrange two movable pulleys A and B and tv.o 
fixed pulleys C and D as in Fig. 21 . The weight is four times the power, 

^ but the power moves four times 
as far as the weight, showing 
that P:IV :: lVd:Pd. 

In all of these experiments 
with pulleys it is shown that the 
number of cords supporting the 
weight is to the number of cords 
supporting the power as the Pd 
is to the IVd. 




-^i^ 



W 




Fig. 21. 



Fig. 22. 



Experiment 23. — Place on a toy wagon a stone of such size that 
wagon and stone together weigh 50 units. Place the w^agon thus 
loaded on an inchned plane (Fig. 22). Fasten one end of a stout 
string to the wagon, and to the other end of the string attach a v^eight 
of such size that \ hen the string passes over the pulley, as in the 
figure, the wagon will remain at rest on the incline. If the length of the 



Work and Energy. 37 

incline AB is twice its height AC, the weight P necessary to balance 
the loaded wagon will be 25 units. It is easily seen from the figure 
that when the power moves a distance AB, the weight moves through 
a vertical distance AC, Thus it is evident that in the case of the in- 
clined plane : — 

P : IV:: height of incHned plane : length of inclined plane, 

or P:W::Wd:Pd. 

The Wedge. — An inclined plane when pushed or driven 
is called a wedge; but as both faces are made slanting, it 
is a double inclined plane. 

Experiment 24. — Cut out a long triangle of paper (Fig. 23) and 

wind it around a lead pencil, first winding on the end BC and keeping 

AC2X right angles to the length of the pencil. 

The side AB will make a spiral around the 

pencil. This spiral corresponds to the thread 

of the screw. Again, press the point of a 

screw firmly down on a table top. Place a 

pencil point in the groove nearest the point 

Fig. 23. 
of the screw. Upon turning the screw from 

left to right the pencil point will rise. These experiments indicate that 

the screw is a form of the inclined plane. 

The Screw. — The projecting ridge around a screw is 
called the thready and the end of the screw to which the 
power is applied is called the head. The distance parallel 
to the axis of the screw between the two adjacent turns of 
the thread is called \\\t pitch of the screw. Manifestly one 
revolution of a screw moves it the length of its pitch. 

The power which causes the revolution is generally 
applied by a lever, and moves through the circumference 
of a circle. 





38 Elements of Physics. 

As in other simple machines P '.WwWd: Pd, so that a 
given power will support a weight as many times as great 

as itself as the circumference of 
the circle described by the power 
is times as great as the pitch of 
the screw. 

Questions. — i . A plank 1 2 feet long 
weighing 48 lbs. is supported by two 
props. One is 3 feet from one end, and 
the other is i foot from the other end. 
What is the pressure on each prop? 
Fig. 24. 2. With a movable pulley what force 

will support a weight of 100 lbs.? 

3. In a wheel and axle 20 lbs. at the circumference balances 600 
lbs. on the axle, whose diameter is 3 inches. What is the diameter of 
the wheel? 

4. What kind of a lever is the nut cracker? 

5. What kind of a lever is a pair of scissors? 

6. Why are tinners' shears short-bladed? 

7. What is the advantage of long-bladed shears? 

8. What kind of a lever is a pair of sheep shears? 

9. What kind of a lever is the forearm? 

10. What kind of a lever does the head represent? 

1 1 . What kind of a lever is the lower jaw? 

12. With a wheel and axle a power of 8 lbs. sustains a weight of 176 
lbs. What is the ratio between the radius of the wheel and that of 
the axle? 

13. Two horses are attached to the levers of a capstan 12 feet from 
its axis. The radius of its axis is 18 inches. If each horse pulls 1000 
lbs., what force is exerted upon the boat? 



Work and Energy. 39 

14. Two weights of 500 and 2000 lbs. are suspended from the 
ends of a lever 20 feet long. Where must the fulcrum be placed that 
they may balance? 

15. A plank 12 feet long is used to raise a barrel of flour into a cart 
3 feet high. What force is necessary? 

16. What is a compound lever? 

17. What kind of a lever is a claw hammer? 

18. Can a man raise himself out of a well with two fixed and two 
movable pulleys as in Fig. 20? If he weighs 180 lbs., what force 
does he exert? 

19. The circumference described by a lever used in turning a screw 
which has 3 threads to the inch is 9 feet. A force of 100 lbs. on the 
lever will exert what force on the screw? 

20. Is there any such thing as a labor-saving machine? 

21. Of how many and what simple machines does a crane consist ? 



CHAPTER IV. 

MECHANICS OF FLUIDS. 

Pressure of Fluids. — Fluids belong to that kind of 
matter in which the attracting and the repelling forces 
sustain such relation to each other 
i!!!i::|.illilliiinv ^j^g^i- lY^Q molecules are free to move. 

Fluids may be either liquids or gases. 
Water and air are types and are 
used to demonstrate all physical phe- 
nomena relating to liquids and gases. 




Fig. 25. 



The action of gravity upon liquids 
is everywhere manifest — in the fall- 
ing rain, the running streams, etc. ; but to perceive its 
action upon the air we must study the question carefully. 
If we place our hand in a pail of 
water, we do not feel the weight or 
pressure of the water upon it ; if we 
dive to the bottom of a pond, we do 
not feel the weight of the water above 
us, as the water tends to make us 
float. If we take a hollow globe full 
of water (Fig. 25), we can appreciate 
its weight ; but if we pour the water 
out of it, can we feel any weight of air.^^ 




Fig. 26. 



Experiment 25. — Fill a test tube with shot and invert it so that the 
shot will run out upon a table (Fig. 26). The shot will spread out 

40 



Mechanics of Fluids. 



41 




over the surface of the table in all directions. This experiment illus- 
trates the condition of the air^ whose molecules are free to act in the 
same manner as the shot, pressing each other in all 
directions. 

Now place the shot in one end of a U-shaped tube, 
and they push up into the other side, as in Fig. 27. 
This shows that the downward pressure in one side 
caused an upward pressure in the other. 

Experiment 26. — Push the piston of a " seven-in- 
one " apparatus (Fig. 28) to the bottom of the cylinder 
and close the stopcock S to prevent entrance of air. 
Try to pull the piston out again. Hold the apparatus ^^* ^^* 

in different positions so that the air may push up, down, and sidewise 
against the piston. No difference will be 
found in the pressure which it receives from 
the different directions, indicating that air 
presses equally in all directions. 

Experiment 27. — Force a tin can which 
has a small hole in the bottom into a pail 
of water (Fig. 29). The water rushes up 
through the hole in a stream, showing that 
the water presses upward. 

Punch a hole in the side and try again. 

Experiment 28. — Fill a tumbler with water and cover the top closely 
with writing paper ; hold the paper in place 
with the palm of the hand, then tilrn the 
tumbler top downward. The w^ater will not 
run out because the pressure of the air up- 
ward is great enough to prevent it. 

Experiment 29. — Fig. 30 is intended to 
illustrate an experiment which proves that p 




Fig. 28. 






42 



Elements of Physics. 



water presses equally in all directions. 

A 



-^ is a glass tube in which is 
a small quantity of 
' colored liquid. B is 
a rubber tube^ and C 
is a small glass funnel, over which is tightly 
stretched a piece of sheet rubber. When the 
funnel is thrust into a pail of water, the pres- 
sure of the water on the rubber causes the 
colored liquid to move out toward the end 
of A. Thrust the funnel into the water, first 
with the rubber down, then on one side, and 
Fig. 30. ^]-^gj^ yp^ ^j^^^ ^Q^^ ^j^g^l- ^^^Yi time the effect on 

the liquid in the glass tube is the same, if the center of the sheet rubber 
is kept at the same depth. 



bI 


V 


t---l 


* 


-^^^^m 


b^^^=:r-^^=— ^-^^^^^^^= 


= = 


^^=^^=^^'^^=^^^E 


-— ^ 



COMPRESSIBILITY AND ELASTICITY OF GASES. 

Experiment 30. — Pull out the piston of an ordinary bicycle pump to 
the end of the cylinder. Press the finger firmly on the orifice, from 
which the air is forced by the pump. Push the piston 
slowly down into the cylinder of the pump, steadily 
decreasing the volume of the air in the cylinder by 
compression. Suddenly remove the force from the 
piston, and it will fly back to its original position. 
This experiment indicates the compressibility and elas- 
ticity of the air. 

Experiment 31 . — Fill a bottle half full of water, and 
place in it a perforated stopper and glass tube (Fig. 31). 
Blow very strongly with the mouth into the bottle. 
When you have blown in all the air you can, suddenly 
remove the mouth from the tube. What happens? 
The water rushes from the tube, as in Fig. 31, because of the elasticity 
of the air. 




Fig. 31. 



Mechanics of Fluids. 



43 



Experiment 32. — Pull the piston nearly out of the seven-in-one 
apparatus (Fig. 28), then close the stopcock. Push 
upon the piston suddenly. What does it show? 

Boyle's Law. — Experiment 33. — In Fig. 32, A 
and B are two glass tubes, connected by a rubber 
tube, R^ and supported on a wooden stand. A con- 
tains the air to be measured, and Zy is a yardstick, 
up and down which B is to move. Mercury is poured 
into the top of B until it fills the tube B^ the rubber 
tube Rj and the tube A^ to approximately the height 
indicated by the darkened portions in Fig. 32. 

If B is lowered till the tops of the mercury columns 
in A and B are on the same level, the air in A re- 
ceives the pressure of one atmosphere; i.e. the mer- 
cury columns in B and A balance each other and 
the pressure on the air confined in tube A is the 
same as that which the air exerts upon the top of the 
mercury column in the open tube B. 

If B is raised till the mercury stands about 30 
inches higher in B than in A., an additional pressure 
of approximately 14.7 lbs. per square inch is added 
to the air in A\ i.e. we have doubled the pressure 
upon the confined air. By measuring we find that 
the volume of the air is only one half as large as it 
was before the pressure was increased. Doubling the 
pressure upon air, then, has halved its volume. 



Many experiments of this sort upon air 
and other gases show that the vohtme of 
a quantity of gas at constant temperaticre 
varies inversely as the pressure to zvJiich it 
is subjected. 



D 

Fig. 32. 



B 



44 



Elements of Physics. 



B 



p 



nx 



Fig. 3^. 



The Air Pump. — Fig. 33 represents an air pump, so 
called because it is used for taking the air out of vessels. 

B represents the bar- 
rel, and R the vessel 
or receiver out of 
which the air is to 
^ be taken. When the 
piston P is raised, 
the downward pres- 
sure of the air on 
the valve V keeps 
it closed, and the air 
in the barrel is pushed out by the rising piston. There is 
now no air in the barrel to exert a downward pressure 
on V\ and the air in the receiver rushes out unopposed 
into the barrel. When P is pushed down, valve V closes 
and valve V opens, letting out the air in B. If this opera- 
tion is kept up, the air will continue to come out of R 
until not enough remains to lift the valve. Such a pump 
will not produce a perfect vacuum. Why } To obtain a 
more perfect vacuum a mercurial pump is used. (See 
^' Mercury Pump " in any encyclopedia.) 

A barometer is sometimes attached to C, in Fig. 33, 
to indicate the pressure of the air remaining in the 
receiver. 

The Mercurial Barometer may be made from a tube closed 
at one end and 86 centimeters or more in length, and a cup 
or dish of mercury. Fill the tube with mercury, being 
careful that no bubbles of air are left in it. Place the 
finger over the open end and invert the tube, placing the 
open end in the cup of mercury. When the finger is 



Mechanics of Fluids. 



45 



removed, the mercury settles from the top, leaving a 
vacuum of a few centimeters (Fig. 34). 

The length of the space at the top of the mercury col- 
umn varies as the air pressure on the surface of the mercury 
in the cup increases or diminishes. 



31 
30 
29 
28 



The vacuum is known as the Torricellian 
vacuum because Torricelli first performed the 
experiment. 

The distance from the top of the mercury 
column in the tube to the surface of the mer- 
cury in the cup will be found to be about ^6 
centimeters, or 30 inches near the sea level, 
and less at higher altitudes ; but it will vary 
on different days, and may be an inch above 
or below the average. 

A column of mercury one square inch in 
cross-sectional area and 30 inches high weighs 
about 15 lbs. Hence the barometer shows 
that the pressure of the air is about 15 lbs. 
per square inch at sea level. 

Another kind of barometer, the aneroid, con- 
sists of a shallow metallic box having a thick 
back and a very thin flexible face. The air is partially 
exhausted and the box is sealed. The atmospheric pres- 
sure on the face operates a clockwork arrangement which 
moves the hand around a scale. 

Questions. — Water is about j'g as heavy as mercury, and glycerine 
is Y^o as heavy. How long tubes must be procured for the construction 
of barometers in which water and glycerine are the liquids employed? 
What advantages and disadvantages would such instruments possess? 




Fig. 34. 



46 



Elements of Physics. 



=p= 



-rB- 



Fig. 35. 



Uses of Barometers. — The barometer is a certain in- 
dicator of all changes in atmospheric pressure. These 

changes generally indi- 
" P^ cate weather changes. 

— ' Low barometer areas 

cross this country from 
southwest to northeast as a general thing, and hence by 
following the indication of the barometer weather predic- 
tions of a general character may be made. 

Rules. ^ — I. The rising of mercury indicates the ap- 
proach of fair weather, the falling of the mercury foul 

weather. Storm centers 
are in the region that 
show low barometer. 



2. A sudden fall in 
the mercury indicates the approach of 
a storm. 

3. A rise of mercury during a stormy 
period is indicative of a clearing up of 
the storm. 




Students should find 
these rules. 



reasons for 



Condenser. — Fig. 35 represents an- 
other type of air pump called a con- 
denser, because it is used to put more 
air into vessels ; for example, a bicycle 
pump. When the piston P is pushed 
into the barrel By valve C closes and 
V opens, allowing the vessel to be 
filled. When P is pulled out of the barrel, the valve V 



Fig. 36. 



Mechanics of Fluids. 



47 



r 


A 
CC 


^=z= 


J- 


H^ j 



closes, preventing the air in the vessel from rushing back, 
and valve C opens, letting air into B, If this motion is 
kept up, the air in the vessel will be very much condensed. 

Pumps for Transferring Liquids. — Fig. 36 represents a 
pump constructed the same as an air pump, and working 
exactly like it except that some liquid is transferred instead 
of air. It is called a lifting pump, because after the water is 
above the piston, it is simply lifted and allowed to run out. 

It is often necessary to raise liquids to a great height, as 
in fire engines, water works, and the like. Such a pump 
as Fig. 36 represents could 
not raise water much more 
than 30 feet. Why.? Hence 
we use a force pump (Fig. 
37) in which the piston has 
no valve, but the barrel has 
a branch pipe leading from 
the lower part to an air-con- 
densing chamber, CC, at the 
bottom of which is a valve, 
F', opening upward. As the piston is 
raised, water is forced up through the 
valve V in the lower part of the barrel 
C by atmospheric pressure, while air or 
water in CC is prevented from returning 
to the barrel C by the valve F^ When 
the piston is forced down, the valve V 
closes, the valve V^ opens, and the water 
is forced into CC, condensing the air above the water. 
The elasticity of the condensed air forces the water out 
of the tube A in a, continuous stream. 




Fig. 37. 



48 



Elements of Physics. 



Transmission of External Pressure. — Experiment 34. — Place your 
thumb over the spout of a force pump, put the lower end of the barrel 
in a jar of water, and then work the machine. The water rushes up 
and pushes out on all sides of your thumb ; so we know that the piston 
transmitted the pressure to the water. 

Experiment 35. — Support a seven-in-one apparatus with the piston 
end upward, force the piston in, and place on it a block of wood, and 
on the block a heavy weight. Attach one end of a long piece of rubber 
tubing to the tube which enters the cylinder, and insert a funnel in the 
other end of the rubber tubing. Open the stopcock, raise the funnel 
as high as practicable, and pour water into it. The piston is forced up, 
raising the weight. 

The Hydrostatic Press. — If a given pressure is added 
to a given area of the surface of an 
inclosed volume of a liquid, that given 
pressure is transmitted to every equal 
area within the containing vessel. For 
example, if a keg is full of water and 

10 lbs.' addi- 
tional pressure 
is appHed at the 
open bunghole, 
which is I square 
inch in area, that 
10 lbs.' pres- 
sure is trans- 
mitted to every 
equal area, so 
that the pres- 
sure upon the 
inside of the barrel is 10 lbs. per square inch more 
than before. Upon this principle the hydrostatic press 




Fig. 38. 



Mechanics of Fluids. 



49 



is constructed. If the small piston P is i square inch in 
area of cross-section, and the large piston P^ is lOO square 
inches in cross-section, a downward force of lOO lbs. on 
the small piston will cause an uplift of 10,000 lbs. on the 
large piston. 

By means of this machine a small force may be made to 
exert a great pressure upon any object, e.g: a bale of cot- 
ton, placed above the large piston. 

Pressure exerted by Liquids Due to their Depth. — A and 

B (Fig. 39) are two bottomless vessels, the holes in the 
bottom being of exactly the same size. A cord is put 
through the hole in vessel B^ then attached to one arm of 
the balance beam. A disk that exactly fits the bottom of 
the vessel h fast- 
ened on the string 
below. A weight 
sufficient to bring 
the disk tightly 
over the bottom 
of B is then 
placed in the 
other pan of the 
balance. Water 
is then poured in 
until the disk is 
pushed down, and the height of the water in the vessel is 
measured. In the same way A is tried, and it is found that 
the height of the column of water that will press the disk 
down in A is the same as in B, although we know that the 
volume in B is greater than in A. So we see that the 
pressure of a liquid depends upon its depth. 




Fig. 39. 



50 



Elements of Physics. 



The Siphon. — Experiment 36. — Fit a small bottle D with a glass 

tube A about 34 inches long, and a rubber tube B about 10 inches 

long, attached as in Fig. 40. With B closed, fill the bottle and A with 

mercury, and invert into the bowl of mercury C. The mercury will run 

out into the bowl until the column stands only 

30 inches high in the tube. Why ? What is in 

the bottle ? What pressure is exerted upon the 

top of the mercury column vn Al If we put 

pressure upon the mercury in A^ what will 

happen? How may we apply such pressure? 

By placing i5 in a vessel of water and open- 
ing it, the mercury will run out into C; but as 
it goes, the water runs up through B and fol- 
lows the mercury, and continues to flow as 
long as B is in the water. The water runs 
through from B to C, because the column of 
water in tube A is heavier than the column 
in^. 

We see, on studying the figure, that there 
is atmospheric pressure on the surface of the 
liquid in E^ tending to force it up the tube B. 
When B^ D, and A are full of water, there is 
in Z^ a force tending to drive the water toward 
C. This force is manifestly equal to atmos- 
pheric pressure less the weight of the column 
of water in B. There is also atmospheric pres- 
sure on the surface of the liquid in C, and in 
D a force tending to drive water toward E. 
This force is equal to atmospheric pressure less the weight of the 
column of water in A. The movement of the water will be in the 
direction of the greater pressure. In D the pressure toward C is 





Fig. 40. 



Mechanics of Fluids. 



51 




Fig. 41. 



greater than that toward E^ by an amount which is the difference 
between the weights of the columns A and B. 

Experiment 37. — Take a bent tube having one arm longer than the 
other, and after filling it with 
water place it ovar the side of 
a vessel full of water, as in Fig. 
41. The column of water XZ 
being heavier than the column 
XYj the water starts running, 
and the pressure of the air upon 
the surface AB (being able to 
sustain a column nearly 30 feet 
high) will keep it running as 
long as the short arm of the 

tube remains in the liquid. Such a tube when used for transferring 
fluids by use of atmospheric pressure is called a siphoii. 

Questions. — i. Name five uses of the siphon. 

2. What causes liquid pressure? 

3. Why does not a person in the bottom of a pond feel the weight 
of the water above him ? 

4. Why is a barometer tube closed at the top ? 

5. Why must the atmospheric air touch the mercury in a barometer 
tube at the bottom ? 

6. The water in a well is 50 feet below the surface of the ground 
and is to be obtained by means of a lifting pump. Describe the 
pump. 

Problems. — i. An aeronaut finds his barometer standing at 20 inches. 
How high is he, and what is the pressure of the atmosphere per square 
inch? 



52 



Elements of Physics. 



2. The area of the piston in a seven-in-one apparatus is 25 square 
inches. The area of the tube is I square inch. What pressure on the 
piston would 10 lbs. on the tube exert.^ 

3. Using a hydrostatic press, a man wishes to exert a pressure of 
25,000 lbs. with a power of 150 lbs. The large cylinder is 260 square 
inches in area of cross-section. What is the area of the small 
cylinder? 

4. A reservoir which supplies a city with water is 150 feet deep and 
is f full of water. What is the pressure on a hydrant 100 feet below the 
bottom of the reservoir if its area is 86 square inches? 

Buoyancy. — Experiment 38. — Suspend from one pan of a balance 
a piece of stone as large as a hen's egg or a weight. Counterpoise this 

stone with weights in the other pan 
of the balance (Fig. 42). Place 
beneath the suspended stone or 
weight a jar of w^ater and raise the 
vessel till the stone or weight is com- 
pletely submerged. The equilibrium 
is immediately destroyed (due to the 
buoyancy of the liquid), the stone 
tending to rise toward the surface 
of the water. 

Buoyancy is the upward 

Fig. 42. pressure which a fluid exerts 

upon a body immersed in it, 

due to the difference between the depth of the top and 

bottom of the body below the surface of the fluid. 

Experiment 39. — Suspend from one arm of a balance beam a cylin- 
drical bucket A, and from A a solid cylinder B, whose volume is exactly 
equal to the capacity of the bucket. Balance or counterpoise these by 




Mechanics of Fluids. 



53 



weights on the other arm of the beam. Submerge B in water (Fig. 43). 
The buoyancy of the water destroys the equihbrium. Fill the bucket A 
with water, and the equilibrium is restored. Now it is evident that the 
cylinder immersed in the water displaces its own volume of water. But 
the bucket full of water is just sufficient to restore the weight lost by the 
submersion. Hence a solid immersed in a liquid is buoyed up with a 
force equal to the weight of the 
liquid it displaces, i.e. the appar- 
ent loss of weight of a body sub- 
merged in a liquid is equal to the 
weight of the liquid which it dis- 
places. 

All fluids possess buoy- 
ancy. 

Specific Gravity. — The 
specific gravity of a sub- 
stance is the ratio of its 
weight to the weight of an 
equal volume of some standard substance. In Physics, 
water is usually taken as the standard substance. 

Experiment 40. — The weight of a given volume of water is 27J 
grams. The weight of an equal volume of mercury is found to be 37 1^ 
grams. Then taking water as the standard of density, the specific 
gravity of mercury is 371 J -^ 27I =13^. An equal volume of alcohol 
weighs 22 grams. Hence its specific gravity is -f^. The specific 
gravity of chloroform is i|, since a volume equal to that of the water 
mentioned above is found to weigh 41 J grams. 

Since it is true that the apparent loss of weight of a body 
submerged in a liquid is equal to the weight of the liquid 
displaced by the submerged body, it is evidently an easy 
matter to find the specific gravity of solids by experiment. 




Fig. 43. 



54 Elements of Physics. 

To find the specific gravity of a solid, weigh the soHd in 
air ; weigh it submerged in water, and divide the weight 
in air by the difference of the weights in air and water. 

Experiment 41. — Submerge a small piece of roll sulphur, weighing 
80 grams in air, in a graduated beaker of water. (It displaces about 
40 cubic centimeters of water.) Weigh the same piece of sulphur when 
submerged in water. The weight under water will be 40 grams. 

80 ^ (80 — 40) — 2, sp. gr. of the sulphur. 



CHAPTER V. 

HEAT. 

Theory of Heat.^ — The molecules of which a body is com- 
posed are believed to be in a state of more or less rapid 
motion. When the velocity of the molecules of a body 
increases, its temperature rises ; when the velocity of the 
molecules decreases, the temperature falls. 

According to this theory, then, heat is molecular motion 
or molecular kinetic energy. 

Source of Heat. — The sun is the original source of all our 
heat. Its molecular energy is constantly given out to the 
universe. The earth receives a small portion of this, uses a 
part of what it gets, and radiates and reflects the remainder. 

Chemical change is a source of heat, — the heat being 
caused by a rearrangement of atoms. Chemical change 
is generally the breaking up of certain compounds to form 
others. This separation of atoms, and their recombination, 
both produce heat. 

Experiment 42. — Cover a few bits of zinc in a test tube with w^ater 
and add a few drops of hydrochloric acid. The water boils on account 
of the heat generated by chemical action, and the tube becomes hot. 
Light a splinter of wood. Combustion takes place, i.e. a chemical 
union of the oxygen of the air with the elements of the wood. Explain 
the burning of a candle or a lamp. 

^ For an account of the development of the present theory of heat see in 
an encyclopedia, Benjamin Thompson (Count Rumford). 

55 



^6 Elements of Physics. 

Experiment 43. — Slake some lime with water. Intense heat is 
produced. How? 

How is plant heat produced? Animal heat ? 

Collision a Source of Heat. — If we lay a small piece of lead 
on an anvil and strike it with a hammer, the lead will become 
flattened, and warm to the touch. If in a similar way we 
pound a nail, it may be made too hot to handle with comfort. 
In this case the energy of the hammer, due to mechanical 
motion, is transferred from the hammer to the nail in the 
form of heat. Blacksmiths used to employ this method in 
starting their fires, the nail getting so hot that it would 
ignite sulphur. Why do steel and flint produce sparks 
when struck together ? How was the flint-lock gun fired ? 

Friction a Source of Heat. — Experiment 44. — Rub a button or 
a coin rapidly over a cloth surface. Rub the hands together. Rub a 
match over a rough surface. Note the result in each case. 

When bearings get hot on a machine, when Indians start 
a fire by rubbing pieces of wood together, when a rope slips 
through one's hands, and when brakes are applied to a car 
wheel, heat is produced, due to friction. Can the mechani- 
cal energy of bodies be used to heat our houses ? Why ? 

Friction is a very common hindrance to motion. The 
apparent destruction of a given amount of motion always 
produces an equivalent amount of heat. The amount of 
motion in a body depends upon its mass and its velocity, 
and is measured in foot-pounds. In all cases the energy 
perceivable as motion disappears, but reappears in an equiva- 
lent amount in the form of heat. 

Mechanical Equivalent of Heat. — Dr. Joule of England 
ascertained the mechanical value of heat in the following 



Heat. 



^1 



manner : He took a copper cylinder filled with water in 
which a number of paddles were made to rotate. The 
paddles were turned by a falling weight (Fig. 44). The 
weight being known, he meas- 
ured the space through which 
it fell, and the difference in 
the temperature of the water 
at the beginning and end of 
the fall. In this way he found 
that a pound weight in falling 
772 feet produced enough heat 
to raise the temperature of one 
pound of water one degree 
Fahrenheit. Later investiga- 
tion has shown that 778 foot- 
pounds are necessary to raise 
the temperature of one pound 
of water one degree Fahrenheit. 
mechanical eqitivalent of heat. 




Fig. 44. 



This number is called the 



Transformation and Indestructibility of Energy. — The 
above experiments and many others prove that when one 
kind of energy disappears it is not destroyed, but reap- 
pears in the same or some other place as another form of 
energy. In the case of sound, the energy of a vibrating 
mass disappears from that mass to reappear in the vibration 
of some medium, or of the ear. When a body is thrown 
upward, its velocity, and hence its kinetic energy, grows 
continually less until it reaches its highest point of flight, 
where it has no motion and no kinetic energy ; at this 
highest point, however, the body has potential energy equal 
in amount to the kinetic energy with which it started from 



58 Elements of Physics. 

the ground. During its rise the body has continually lost 
kinetic and gained potential energy. As the body falls it 
loses potential and gains kinetic energy until it reaches the 
ground, where its kinetic energy is equal to the potential 
energy which it had at its highest point ; neglecting, of 
course, any transformation of kinetic energy into heat 
through friction of the air during the body's fall. 

Furthermore, when the body is stopped by the earth, its 
kinetic energy is changed to heat and the temperature of 
the body is raised. 

The Conservation of Energy. — Matter, we have learned, 
is indestructible, so that when a certain form disappears it 
is always found manifest in some other form. Matter has 
been defined as that which has extension and weight, and 
can be perceived by the five senses. We are enabled to see 
the truth of the above statement only through that manifes- 
tation of matter called energy; hence, matter being inde- 
structible, we must infer that its principal manifestation — 
energy — is indestructible. For instance, the heat of a 
steam engine is converted into motion, the motion is carried 
to a dynamo, the revolution of the dynamo armature de- 
velops electricity, which is transferred by wires to a street- 
car motor and there transformed into motion. The motion 
of the motor is carried to the wheels and car, thereby over- 
coming the force of gravity and inertia. A part of the elec- 
tricity from the dynamo is converted into heat, and a part 
gives light for the car; nothing is lost, only transformed. 
So it is with every form of energy. This great principle 
is known as the conservation of energy ; it means that the 
total ene7^gy of the unive^^se is a constant qnantity, never 
more or less no matter what changes it may pass through. 



Heat. 



59 



Transference of Heat. — Heat has a tendency to pass 
from a warmer to a colder body until there is an equality 
of temperature between the two. If two bodies of different 
temperatures are placed in contact, the hotter loses heat to 
the colder until the two are at the same temperature. 

There are three methods or processes by which heat is 
diffused or transferred: (i) conduction, (2) convection, 
and (3) radiation. 

Conduction. — Upon placing one end of an iron wire or rod 
in the fire and holding the other end in the hand a rise of 
temperature is soon perceived. The temperature of a body 
depends upon the rate and amplitude of the vibration of 
its molecules. In case of the rod the molecules of the part 
which is in the fire are quickened in vibration, hence they 
strike the neighboring molecules more vigorously, trans- 
ferring to them their own motion, and these neighbors are 
driven against the next molecules, and so on until all the 
molecules in the rod are affected. The transmission of 
heat from one part of a body to another without perceptible 
motion of matter is called conduction. Bodies which allow 
heat to pass along them in this manner are called condnctoi's. 

Experiment 45. — Take two or three wires of the same length and 
size, but of different materials, and twist them together at one end, then 
fasten little balls of wax on 
them at equal distances from 
the twist (Fig. 45). Now 
hold a flame at the twisted 
end and note the effect on 
the wax balls. 



Experiment 46, — Hold 
one enci gf a short glass 




Fig. 45. 



6o Elements of Physics. 

tube in a flame. The part that is in the flame becomes very pliable 
before the glass transfers enough heat to make it unpleasant for the 
hand. 

Experiment 47. — Fill a long test tube about three-fourths full of 
water. By holding it at the bottom and allowing a flame to strike the 
side about halfway to the surface of the water^ violent boiling may be 
caused without the bottom becoming warm. Explain. 

These experiments teach that some substances conduct 
heat much better than others. Those which conduct heat 
rapidly are called good conductors, the others poor con- 
ductors. Bodies that do not thus allow heat to pass along 
them are called non-conductors. Such substances are very 
rare, though it is difficult to show that pure dry air has 
any conducting power. However, the term *' non-con- 
ductor" is used to mean those substances which conduct 
heat very slowly. 

Generally speaking, solids are better conductors of heat 
than liquids, and liquids better conductors than gasqs. 
Among solids metals are the best conductors, and of the 
metals silver and copper the best conductors. 

Questions. — i. Why on a cold morning in winter does a piece of 
iron feel so much colder to the hand than a piece of wood or cloth ? 

2. Why can one hold the hand in the hot air of an oven without 
harm and yet get a severe burn from contact with the metal upon the 
sides of the oven ? 

Experiment 48. — Press down upon the flame of a lamp or Bunsen 
burner a piece of fine wire gauze. Note that the flame does not pass 
through the gauze. Hold a piece of wire gauze an inch above the top 
of a Bunsen burner. Turn on the gas and hold a lighted match above 
the gauze. The gas burns above the gauze, but not below- Explain. 



Heat. 



6i 



Look up in an encyclopedia the Davy safety lamp and the Norwegian 
cooking box. 

Experiment 49. — Fill a large test tube with water. Sprinkle in the 
water a little fine sawdust. Hold one side of the bottom of the tube in 
the flame of a lamp or Bunsen burner. Note the circulation of the water. 

Experiment 50. — Light a lamp and. 
hold the hand at a given distance upon 
every side successively, and finally above 
it ; determine where you find the highest 
temperature. Now place the chimney on 
the lamp and hold a smoking paper just 
beneath the edge of the burner; note the 
result. 



f^ ^ 




Fig. 46. 



Experiment 51. — Bore holes in a 
cigar box at A and B, as in Fig. 46, 
Place a lighted candle at A, then cover 
each hole with a lamp chimney. Hold a smoking paper at C and note 
the result. This shows how coal mines and the like are ventilated. 

Convection. — The air around any source of heat, on 
becoming heated, expands rapidly and becomes less dense 
than the surrounding colder air, hence the colder air press- 
ing in from all sides pushes the warm air upward and takes 
its place. This passage of heat by actual transmission of 
heated molecules is called convection. 

Ventilation. — Physiology teaches us that in order to 
have good health we must have an abundant supply of 
fresh air, and that we may have this we must have a con- 
tinual circulation of air in our rooms, i.e. we must have ven- 
tilation. Any system of ventilation to be of value must, 
without strong draught, bring into rooms a large amount of 



62 



Elements of Physics. 



pure air and carry off the impure air. Fig. 47 represents 
a practical scheme for heating and ventilating a one-room 
schoolhouse. The source of heat is an ordi- 
nary stove. The stovepipe is jacketed with 
a metal cylinder which extends through the 
floor and outer wall of the building as shown 
by the figure. When a fire is started 
in the stove, the air in the upper part 
of the jacket becomes heated, causing 
the outdoor air to flow in. This scheme 
insures the entrance of a plentiful sup- 
ply of pure, warm air. 

By jacketing the extreme top portion 
of the stovepipe and 
carrying this jacket 
into the chimney, a 
provision may be 
made for the removal 
of impure air. 

Radiation. — Upon 
allowing the sunlight Fig. 47. 

to enter a dark room 

through a very small opening it will be seen by means 
of the dust which fills that portion of the air when two 
chalk erasers are tapped together near the opening, that 
light passes in straight lines. If the hand be held in the 
path of this light for some time, the hand will become 
heated. When we place a radiometer (Fig. 48) in the sun- 
light, it begins to rotate ; we know that energy must have 
been imparted to it, because energy is always necessar)^ to 
produce motion. That which we receive from the sun must 




Heat. 



63 



be energy in some form, whether it affects our senses or 
produces chemical changes. 

The Radiometer consists of a bulb from which a large part of the air 
has been exhausted, and an axis or spindle with four vanes of aluminum 
or mica attached to it. The vanes are blackened on one side and 
silvered on the other. When exposed to the 
sunlight or to any other source of heat, the 
vanes begin to revolve with the polished faces 
in advance. The reason for this is, that the 
blackened faces absorb more heat than the 
polished ones and acquire a higher tempera- 
ture ; the air molecules which strike the vanes 
bound off from the blackened faces with greater 
velocity than from the polished ones, and by 
reaction give the vanes an impulse in the direc- 
tion indicated. 

Ether. — The question naturally 
arises, '' How does this energy come to 
us .-^ " The depth of our atmosphere is 
very small compared with our distance 
from the sun, hence it is necessary to 
assume that there is some other medium 
for the transmission of solar energy 
through our interplanetary spaefe ; there 
must be, in fact, a medium permeating all space. This 
medium is called ether, and by the motion of its parts heat 
can be transmitted from one place to another. Many phe- 
nomena in nature can be accounted for upon no other 
hypothesis ; hence our belief in this all-pervading medium. 

The transmission of heat or light from any source through 
the ether is called radiation. One might say that the 




Fig. 48. 



64 Elements of Physics. 

transmission of heat is always by radiation, although techni- 
cally a distinction is made between the transfer at appreci- 
able distances and the transfer by contact. In. convection 
the transfer is a mechanical one, and is not in any way 
connected with the change in the temperature of the body 
carried, because after the body in which the heat exists 
is transferred, there must still be a transfer of the heat 
from the heated body before it can be utilized as heat. 

Effects of Heat : Expansion. — The hotter a body be- 
comes, the more active are its molecules. This increased 
activity of the molecules causes them to occupy more space, 
producing an expansion of the body. 

Experiment 52. — Take a brass ring and a ball that will just pass 
through it. Pass the ball through the ring, then heat the ball and try 
to pull it back through the ring. What have you learned? How may 
the ball be passed through the ring while still hot.^ 

Experiment 53. — Take a flask fitted with a perforated stopper and 

tube (Fig. 49). Place the flask above a lighted lamp with the tube 

B lowered into a vessel of 

water. The heat from the 

lamp will cause the air 

within the flask to expand, 

and some of it will force 

its way out, causing bubbles 

to rise to the surface of the 

water. 
Fig. 49. 

To flirther illustrate the 

fact that heat causes air to expand, place a cork in each end of a small 

glass tube and apply heat to the tube. The expansive power of the 

inclosed air will soon blow one of the corks out. 




Heat. 65 

Experiment 54. — Partly fill the flask (Fig. 49) with water and push 
the tube B below the surface of the water in the flask. Apply heat, and 
the water will rise in the tube. Does heat cause all substances to expand 
at the same rate? 

Experiment 55. — Take strips of iron and brass of the same di- 
mensions, and rivet them together, forming what is called a compound 
bar. Heat the bar evenly throughout its length and account for wdiat 
happens. 

Experiment 56. — Take two flasks, and fill one with water and one 
with alcohol. Fit glass tubes in them, as in Fig. 49, then place in a 
dish of hot water. It will be noticed that the alcohol will rise more 
rapidly than the water. By taking flasks of air and hydrogen instead 
of water and alcohol, similar results will be noticed. 

The foregoing experiments show that heat expands 
soHds, liquids, and gases. Further experiments similar to 
the above show that each solid and liquid substance has a 
rate of expansion of its own, but that all gases expand at 
practically the same rate. 

When heat is applied to a body, the effect produced 
varies with the nature of the body. In any case there is 
a rise in temperature. If the body is a solid, it may fuse or 
liquefy when heat is applied for a sufificiently long time. 
Liquids may be vaporized by the continued application of 
heat. Some bodies like wood and coal do not fuse or 
liquefy, but are decomposed into their constituent elements 
or compounds. If heat is removed from bodies which do 
not decompose, the above changes take place in reverse 
order. 

Thermometry. — Application of the foregoing effects of 
expansion is made in the construction of thermometers. 



66 



Elements of Physics. 



Owing to the imperfection of our senses we are unable 
to measure temperatures by the sensations of heat and 
cold, and for this reason we turn to the physical effect of 
heat upon matter. Liquids are well suited for the expan- 
sive substance of thermometers ; but air and some metals are 
used in certain cases. Mercury and alcohol are the liquids 
most frequently used — mercury because of its high boil- 
ing point, and alcohol because of its low freezing point. 



100 



F 



212 



A Thermometer usually consists of a glass tube of capil- 
lary bore, at one end of which a bulb is blown. That a 
thermometer may indicate definite temperatures, there must 
be some fixed point from which to reckon the expansion or 
contraction. Happily nature furnishes two such points, as 
pure water under the same conditions always boils at the 
same temperature and always freezes at the 
same temperature. To make the scale or 
graduate a thermometer, the bulb and part 
of the tube is filled with mercury (or other 
suitable liquid) and the whole is heated until 
the mercury boils and its vapor expels the 
air from the tube, which is then sealed and 
allowed to cool. The bulb is now placed 
in boiling water, under ordinary conditions 
at the sea level, and the point to which the 
mercury rises is marked ** boiling point.'* 
The tube is then put into a vessel of melt- 
ing ice, or freezing water, and the point at 
which the mercury stops is marked *' freezing point." The 
space between the freezing point and the boiling point is 
divided into a number of equal spaces, depending upon the 
kind of thermometer desired. 



I 







32 



-0 



Fig. 50. 



Heat. 



67 



Fahrenheit and Centigrade. — The two usual thermom- 
eter scales are the Centigrade and Fahrenheit (Fig. 50). 
In the Centigrade the freezing point of water is 0° and the 
boiling point loo"^ ; in the Fahrenheit the freezing point 
is 32° and the boiling point 212°. In the Centigrade there 
are 100 spaces or degrees, and in the Fahrenheit 180 spaces, 
between freezing point and boiling point. Hence, 1° C. 
equals f "^ F. If a Fahrenheit thermometer reads 60°, the 
actual temperature is 60— 32, or 28"^ F. above the freezing 
point ; but 28° F. equals f of the corresponding Centigrade 
reading, which is found to be i5|° C. To find 
Centigrade reading from the Fahrenheit, sub- 
tract 32 from the reading Fahrenheit and mul- 
tiply the remainder by f ; and to find the 
Fahrenheit reading from the Centigrade, multi- 
ply the Centigrade reading by f and add 32. 
(See Fig. 51 for Centigrade scale.) 



Maximum and Minimum Thermometers. — 

There are two special kinds of thermometers, 
called the maximum and the mmimttm.. One 
variety of maximum thermometer is like an 
ordinary mercurial thermometer, except that the 
tube has a narrow place in it near the bulb 
through which the mercury is forced by expan- 
sion as the temperature rises. When the tem- 
perature falls and the mercury contracts, the 
weight of the portion of mercury in the tube 
above the point of narrowing is not sufficient to force it 
down through the very small orifice, and it remains until 
shaken down, thus marking the position of the column for 
the greatest expansion, i.e. the highest temperature. This 





A 




"Ia^ 






W 




l50-i 


g 




140-i 


g 




130-1 


g 




120-1 


B 




II 0-1 


g 




100-1 


1 




90-1 


a 




80 


g 




70 


g 




60 


a 




50 


1 1 




40 


1 




30 












za 






10 






0- 






lO- 






zo- 






30. 






40. 






50- 






60 






1 


■ 









FIG. 51. 



68 



Elements of Physics. 



thermometer is used by physicians. A thermometer con- 
siderably larger than the clinical or physicians, but made 
on the same plan, is used by the United States Weather 
Bureau. The Weather Bureau also uses the minimum 
thermometer, which is filled with alcohol and has a tube 
of rather large bore. Within the tube is a glass rod which 
extends below the surface of the alcohol and is pulled down 
by the surface film as the temperature falls and the liquid 
contracts. When the temperature rises again, the alcohol 
flows past the index and leaves it to mark the lowest tem- 
perature reached. 

Thermometers are sometimes made by fastening two 
metals of unequal expansion together in such a way that as 
the temperature changes, their position changes 
and moves an index which points to a scale 
of degrees. When it is necessary to ascertain 

very high tem- 
peratures, i.e. 
thousands of de- 



grees, thermom- 
Pj(2 ^2 eters are made 

of some metal 
or mineral whose melting point is extremely high. In 
Fig. 52 a bar of metal, AB, is fastened at one end and 
is free to expand lengthwise ; in so doing it moves the 
index lever, C, indicating the temperature. 

Other Applications. — There are many other practical 
applications of expansion and contraction. Tires are put 
upon carriage wheels while hot, and as the tires cool 
they contract so much as to fit very tightly. The steel 
jackets which strengthen the barrels of large guns are 




Heat. 69 

''shrunk on," i,e, put in place while hot and allowed to 
tighten themselves by the contraction which comes in 
cooling. The gridiron pendulum is so constructed of 
brass and steel bars, which expand at unequal rates, that 
the length of the pendulum is kept practically unchanged 
by changes in temperature. In laying steel car rails it is 
necessary to leave spaces between the ends of the rails to 
allow for the expansion which is produced by hot weather. 

Exceptions. — We have already mentioned the fact that 
as a rule the addition of heat to a body causes it to expand. 
Of course the removal of heat from a body causes contrac- 
tion. There are a few exceptions to this rule that are 
worthy of note. 

If warm water be cooled, it will contract in accordance 
with the general rule until it reaches a temperature of 
4° C, when it begins to expand and continues to do so until 
it freezes. Ice is, then, not as dense as water, and water 
is densest at 4° C. Cast iron and type metal also expand 
on solidifying, and for this reason are especially adapted 
for casting, since they fill every portion of a mold. 

Expansion of Gases. — We have already learned that all 
gases expand at practically the same rate when heated. 
It is not a difficult matter to determine the rate of expan- 
sion by experiment. If the volume of a quantity of gas 
be measured when its temperature is o"" C. and the tempera- 
ture then raised to 1° C, the increase of volume for the one 
degree rise of temperature will be found to be about 273 of 
the volume at 0° C. Two degrees rise of temperature will 
give an increase in volume which is 273 of the volume at 
o°C. 



70 Elements of Physics, 

If the temperature of the gas be lowered 2° C, the de- 
crease in volume will be ^ys ^f ^he volume at o°C. ; if it 
be lowered 10° C, the decrease will be 2W of the volume at 

For each degree that a gas is warmed above o°C. it 
increases 2T3 of the volume measured at 0° C, and de- 
creases at the same rate on cooling. This fact or law is 
frequently called the Law of Charles, 

If a gas loses ^73 of its volume when cooled 1°, it would 
lose III, or its entire volume, when cooled 273°, or to 
— 273° C. Of course a gas cannot contract to nothing. 
Matter cannot be destroyed, but before so low a tempera- 
ture as — 273° C. is reached every gas becomes liquid and 
the rate of contraction is slower. 

This point, — 273° C, is indicated in other ways as the 
point of no molecular motion and hence of no heat ; it is 
called absolute zero. 

Specific Heat. — A unit frequently employed in measur- 
ing heat is the amount of heat necessary to raise the tem- 
perature of one gram of water 1° C. 

The ratio which the amount of heat necessary to raise a 
given weight of a substance one degree bears to the amount 
of heat necessary to raise the same weight of water one 
degree is called the specific heat of the substance ; e.g. if 
the amount of heat needed to raise a piece of lead 1° C. is 
found to be .03 as much as the amount of heat needed to 
raise the same weight of water i°C., the specific heat of 
lead is .03. The specific heat of water is very high, higher 
than that of almost any other substance except hydrogen 
gas. This means that it takes a relatively large amount of 



Heat. 71 

heat to raise the temperature of a mass of water i°C., and 
that the amount of heat given out by a mass of water in 
cooHng 1° C. is large ; i.e. water has great capacity for heat. 
A bottle full of hot water will give out more heat than a 
soapstone of the same weight and temperature. 

Experiment 57. — Place an iron pound weight in boiling water for 
several minutes, then immediately in a pound of water whose tempera- 
ture is known. When the iron and water become the same temperature, 
it will be found that the iron has fallen about ten times as many degrees 
as the water has risen in temperature. Since the amount of heat lost 
by the iron is equal to the amount of heat gained by the water, this 
experiment shows that the heat needed to raise a pound of water one 
degree will raise the temperature of a pound of iron ten degrees ; i.e. the 
specific heat of iron is .1. 

Experiment 58. — Take a pound of water and heat it just one min- 
ute, noting the exact number of degrees its temperature rises, then take 
a pound of some heavy oil, and over the same flame raise its tempera- 
ture to the same point, noting the exact time it takes. It will be found 
that the oil rises in temperature faster than the water ; i.e. it takes less 
heat to raise its temperature one degree than it does to raise the tempera- 
ture of water one degree, hence its specific heat is less than that of water. 

Experiment 59. — Keep a piece of ice in boiling water until it is 
about half gone, then skim it out and compare its temperature with that 
of another piece of ice not so treated. Does heat warm ice ? 

Latent Heat of Melting. — From the above and other 
experiments it is found that tJie melting poiiit is always tJie 
same for the same sitbstance when the pressiti'e remaifis 
constant^ but that it may vary widely for different sub- 
stances ; and that the temperature of a substance remains 
the same during the entire process of melting or of solidi- 



72 Elements of Physics. 

fying. As soon as a solid becomes a liquid its tempera- 
ture begins to rise. Although much heat goes into a body 
during fusion, it is not appreciable, but is all used in 
changing the body from a solid to a liquid without raising 
the temperature. 

The heat which disappears or is used in changing a 
solid to a liquid at the same temperature is called latent 
heat of melting. The latent heat of melting of ice is 80 
heat units ; i.e. as much heat is required to change one 
pound of ice at 0° C. to one pound of water at 0° C. as would 
be needed to raise the temperature of one pound of water 
from 0° C. to 80° C. 

The high latent heat of melting of ice is useful to us in 
many ways. It is said that a block of ice which weighs 
20 pounds will, while melting in a refrigerator, absorb heat 
enough to lower the temperature of 40 pounds of butter 
from 80° F. to 40° F. 

Since vegetables freeze at a lower temperature than 
water, farmers sometimes put tanks of water in their 
cellars in cold weather in order that the heat given out by 
the water in freezing may warm the air to a temperature 
above the freezing point of the vegetables. 

The low temperature secured by the use of a mixture of 
ice and salt is due to the fact that both the ice and salt 
liquefy, and heat is used up in the liquefaction of both. In 
an ice-cream freezer, this heat comes mainly from the cream. 

Evaporation. — Evaporation is a form of vaporization, 
but the term is used to designate that form of vaporization 
which takes place quietly and slowly at the surface of a 
liquid. Although heat hastens evaporation, it takes place 
at all temperatures; even ice and snow evaporate, and clods 



Heat. 73 

in the fields become dry and crumble when the temperature 
is many degrees below the freezing point of water. 

The rapidity of evaporation increases with the tempera- 
ture, dryness of the air, velocity of the wind, amount of 
surface exposed, and the decrease of pressure upon the 
surface. The fact that evaporation is more rapid when 
the pressure is small, is made use of in the vacuum pans 
used in the manufacture of sugar. Many of the ingredients 
burn at a very low temperature, hence without the use of 
vacuum pans the making of sugar and syrup would be 
very difficult. Why does evaporation reduce temperature ? 

Boiling. — When vaporization is hastened by the appli- 
cation of heat beneath the liquid until violent bubbling 
occurs, the phenomenon is called boiling. This boiling is 
occasioned by vaporization throughout the liquid, and not 
at the surface alone, as in evaporation. 

Experiment 6o. — Take a flask about half full of water and place 
in it a stopper having two holes, through one of which a thermometer 
is passed (Fig. 53). Apply heat and note the temperature 
at intervals for some time. The thermometer will rise 
until the w^ater boils, and then become stationary. Now, rfi, 

in the other hole of the stopper, place a glass tube to ""I 

which is attached a soft rubber tube. Let the water boil J I 

again, then pinch the rubber tube so as to confine the steam, /^ ^ 
and compare the temperature with the above. Now re- W^^^^^ 
move the perforated stopper, and when the water is boiling \\y/T 

vigorously put in a solid stopper, quickly remove the flask jl 

from the flame, invert it, and then quietly lay a cold wet '^ 

cloth upon the bottom and account for what happens. 

Dissolve a tablespoonful of salt in the water and compare the 
boiling points. 



74 Elements of Physics. 

Thus we are taught that the boiling point of a liquid 
varies with the pressure upon its surface^ and with the 
density of the liquid. 

The heat used up in changing water at its boiling tem- 
perature into steam at the same temperature is called the 
latent heat of vaporization. The latent heat of vaporiza- 
tion of water is large, — about 535 thermal units. 

Question. — Why does sprinkling a veranda with water on a hot day 
cool the air ? 

Distillation. — If it is required to separate any liquid from 
a solid dissolved in it, in such a manner that the liquid may 
be saved, the operation may be performed by distillation. 
During this process the solution must be heated in a retort, 
or boiler, called a '' still," in the top of which is a pipe for 
carrying away the vapor as it rises. This pipe leads to a con- 
denser, — a very long coiled tube around which cold water 
constantly flows, — and here the vapor is liquefied and col- 
lected in a suitable receiver. The solid previously held in 
solution is left behind in the retort. By the same, process 
two or more liquids may be separated, since some boil at a 
lower temperature than others. It is thus that alcohol and 
other volatile liquids are separated from water. 

Questions. — What are the different principles upon which distillation 
is based? What is a volatile liquid? 

Artificial Cold. — The fact that expansion of a gas lowers 
the temperature of surrounding bodies by absorbing their 
heat has led to some important industries. It was long 
ago observed that when a gas was compressed so as to 
reduce its volume very greatly it became hot. Experiments 
have shown that if a gas thus compressed be cooled down 



Heat. -jK, 

and then allowed to expand rapidly to its original volume 
its temperature will drop to a very low. point. From this 
principle many methods of producing artificial cold for 
refrigeration have been developed, including the manu- 
facture of artificial ice, cold storage, and liquid air. 

Artificial Ice. — The making of artificial ice has in recent 
years developed into an important industry. The cooling 
is accomplished by the use of some very volatile liquid, 
such as ammonia, sulphur dioxide, or ether. These com- 
pounds vaporize very rapidly and at low temperatures, and 
in so doing absorb heat very rapidly. The liquid most 
commonly employed is anhydrous ammonia, which boils at 
27° F. This is, in some factories, forced through long 
coils of pipe submerged in a brine tank. The heat of the 
brine boils the ammonia, and heat is then absorbed from 
the brine or direct from the water to be frozen. In either 
case the vaporization takes place in a cooling coil usually 
placed around the can of distilled water which is to be 
frozen. The rapidity with which vaporization takes place 
in the cooling coil is very great. A compressor driven by 
an engine now receives the gas and by the use of great 
pressure condenses it. When reduced to a liquid state it 
is again forced through the coil. This process takes about 
64 hours at a temperature of from 16"^ to 18"^ F. to freeze a 
can of water weighing 300 pounds. This is the principal 
means of obtaining cold storage. 

Liquid Air. — The principle of cooling by expansion is 
the basis of every system for liquefying air. Mr. Charles 
E. Tripler of New York, a most successful experimenter 
along this line, employs air as the expanding agent to chill 
itself down to the extreme degree of cold required to 



76 



Elements of Physics. 



A' 



B' 



E 



E 



liquefy it, i.e. 312° F. below zero, or 344 degrees colder 
than ice at melting. 

In view of the foregoing principle we see that air is a 

gas because of its 
enormous amount of 
latent heat. Take 
away a sufficient 
amount of this heat, 
and the air becomes 
a liquid ; we may in- 
fer, therefore, that if 
the cooling were con- 
tinued the air would 
become a solid. The 
process of taking 
away this heat is 
accomplished by Mr. 
Tripler as follows : — 
In Fig. 54, /? is a 
cylinder for compres- 
sing the air which 
enters through the 
piston P. The pres- 
sure applied is about 
2500 pounds to the 
square inch ; hence 
the air has a very 
high temperature. 
This compressed air is forced into the tubes A, B, and C, 
where it is cooled to about 50° F. by means of cold water 
flowing through the tank TT. It is then carried over 
into other tubes A ^ B\ C , which are placed in a cylinder 



B 



D 



Fig. 54. 



t 



Heat. J"] 

EE about 15 feet long and 2 feet in diameter, open at the 
top and surrounded by felt or some other poor conductor 
of heat. Along the sides of the tubes A^ and C is a row 
of very small holes opening toward B\ These holes may 
be closed and opened at will, so that when the tubes are 
full of compressed air and the holes are open, the air 
rushes out, strikes against B\ expands very rapidly, and 
passes out at the top of EE. The rapid expansion of the 
air as it rushes out absorbs heat from the air in B^ and 
condenses the latter into a liquid which may be drawn out 
by the faucet F whenever desired. 

A cubic foot of liquid air contains 800 cubic feet of 
gaseous air at sea level ; its tendency to return to its natural 
state is very great ; hence when left in an open vessel it soon 
disappears. When first poured out the liquid air might be 
mistaken for boiling water, as it boils violently. If poured 
upon iron or ice, it vaporizes with explosive violence. In a 
quiet state it resembles pure water except that it has a pale 
blue tint. As a freezing mixture its power is terrific ; it 
freezes pure alcohol very readily, and freezes mercury so 
hard that nails may be driven into wood with it. Iron when 
placed in it becomes as brittle as glass, and an egg frozen 
in it becomes like a mineral egg as hard as quartz. It will 
sear the flesh, and may be used for cauterizing in surgery. 
Many other things are claimed for it, but on account of 
the difficulty experienced in its manufacture, handling, and 
transportation, many years may elapse before it is put to 
any commercial use. 

Applications of Heat in producing Mechanical Motion. — 

Since the amount and rate of evaporation depend upon 
the heat applied and the pressure, we may produce extreme 



78 



Elements of Physics. 



tension upon any expanding fluid and by means of any 
expanding fluid. Upon the tension thus produced, whether 
acting continuously or instantaneously, depends the work- 
ing of many important machines. These machines might 
properly be called heat engines because the elastic force of 
any fluid is entirely due to heat. 

Steam Engine. — The three principal parts of any steam 

plant are the furnace, boiler, 
and cylinder. Fig. 55 rep- 
resents the parts of the cylin- 
der with its steam chest, etc. 
Steam from the boiler enters 
the steam chest at A^ passes 
through B into the cylinder, 
and pushes up the piston Py 
forcing out exhaust steam 
through C and D. 

As the piston gets near the 

top of the cylinder the valve 

rod B, by a device not shown 

in the figure, moves the valve 

down so that live steam enters C, pushing the piston 

back, and exhaust steam goes out through B and D. 

The motion of the piston is communicated by a driving 
rod to the machinery to be run. 

The unit for measuring the work done by a steam 
engine is called a horse-power. This equals 33,000 foot- 
pounds per minute, and is the standard wherever the 
English foot and pound prevail. The work is usually 
measured by the expansive force of the steam exerted 
upon the area of the piston ; then P x A equals the total 
pressure. Now if L equals the length of the piston 




Fig. 55. 



Heat. 79 

stroke, and N the number of strokes per minute, the 
number of foot-pounds of work the engine can do will 
equal P x L x A x N, and the horse-power of the engine 
will h^ P X L X A X A^ divided by 33,000. 

Example. — The piston of an engine is 18 inches in diameter and has 
a 30-inch stroke. What is the horse-power if it makes 20 strokes per 
minute and the gage indicates 50 lbs. per square inch? 

Hot-air Engines. — Hot-air engines are of two classes, — 
those which get their supply of air directly from the at- 
mosphere and discharge it directly into the atmosphere, and 
those which use the same air repeatedly. In both kinds 
the air is first heated and by a special air pump is discharged 
into a main cylinder where the main piston is to be driven. 
At the same time that the hot air is passed into the main 
cylinder, a new supply is passed into the heater. All hot- 
air and gas engines have a *^ water-jacket " cylinder so 
arranged that cold water may circulate directly around the 
main cylinder and thus keep it cool. 

Gasoline Engines. — There are many forms of gas engines, 
but the most important of these, and the one having the 
most extensive use to-day, is the gasoline engine. This has 
a water-jacket cylinder very much like the hot-air engine, 
and gets its power by utilizing the explosive force of gaso- 
line. In one end of the cylinder is a device for producing 
an electric spark and another for regulating the supply of 
gasoline. The machine is started by hand, and this initial 
motion starts the supply of gasoline which the electric 
spark explodes behind the piston, thus driving it forward. 
The heavy fly-wheels carry the driving rod beyond ** dead 
center " and prevent the engine from reversing. When the 



8o Elements of Physics. 

electric spark is not used, a gas torch is provided, and this 
keeps a rod, which extends into the cylinder, red hot. 
The heat of this rod explodes the gas as the spark would. 

Naphtha Engines. — In the ordinary gas engines no 
boiler is used, but in the naphtha engine naphtha instead 
of water is used in the boiler, and instead of coal as a fuel. 
The specific heat of naphtha is very low, hence it becomes 
hot very rapidly. It also vaporizes more rapidly than 
water. These facts make it a very efficient source of 
power, except where a great amount is needed. Large 
quantities of the liquid are difficult to handle with safety. 

In the study of the foregoing applications of heat we 
cannot fail to notice that these furnish notable examples 
of the conservation of energy. Heat is transformed into 
mechanical motion through the agency of some expanding 
medium, as steam, air, etc., so it is really the radiant energy 
of the sun which has been stored up in the coal-beds and 
petroleum reservoirs for thousands of years that is to-day 
moving our trains, ocean steamers, and machinery. 

Questions for Review. — i. What theory of heat is here mentioned? 

2. Name the sources of heat, and give examples. 

3. Define temperature. 

4. What is a thermometer? 

5. Why does the mercury fall when a thermometer is first thrust 
into boiling water? 

6. What is the general effect of heat? Give exceptions. 

7. What are maxhnum and minimum thermometers? 

8. When is a body hot ? 

9. In what ways may heat become equalized? 



Heat. 8 1 

10. When ice begins to melt, why does it not all liquefy at once? 

11. When metals begin to melt, they liquefy at once. Why.? 

12. Why pack ice in sawdust ? 

13. Why does a draft extinguish a flame? 

14. What kind of teakettles are best suited for rapid heating? Why? 

15. Which wall heat more quickly, rough or polished surfaces? 

16. On top of high mountains sunshine is too hot and shade too 
cold. Explain. 

17. Why call any point absolute zero? 

18. Why do late spring snows not cover stone walks the same as 
board walks ? 

19. Which is cooler in summer, light or dark clothing? Why? 

20. Why are steam cylinders polished on the inside? 

21. Why are tumblers broken by pouring hot water into them? 

22. Why does the coming of clouds frequently make it warmer? 

23. What is the temperature F. when it is — 18° C. ? 

24. How do we know that heat is energy? 

25 . What is the mechanical equivalent of heat ? What does it mean ? 

26. How does water in a cellar keep vegetables from freezing? 

27. What is a good system of ventilation? 

28. What is the basis of all cooling mixtures? 

29. Why is so much energy apparently lost in the steam engine? 

30. Why are " governors ^' placed upon steam engines? 

31. Why do railroad engines have a polished sheet-iron jacket 
around the cylinders and boiler? 

32. What determines the power of an engine? 

33. Upon what do the forms of matter depend? Illustrate. 



CHAPTER VI. 

LIGHT. 

Light. — A study of our everyday experiences shows 
that we see objects by the aid of something which comes 
from them to the eye ; that this agent is given out from 
the sun and other bright objects; and that so far as ex- 
periment shows, it emanates permanently and in large 
quantities only from hot bodies. This agent we call 
light. Its principal source is the sun. 

From whatever source light emanates, it proceeds in 
straight lines, with a definite velocity, and apparently suf- 
fers no loss by transmission through any distance how- 
ever great. It is true that its intensity, or the quantity 
that falls on a unit of surface, diminishes inversely as the 
square of the distance from its source, but this does not 
mean that the total quantity is any less, but that it is 
spread over a greater area. 

Experiment 6i. — Take a piece of cardboard and cut a square inch 
out of it, then hold it a foot from a flame, so that the hght may pass 
through the hole and fall upon a screen at 2 feet from the flame. 
Measure the area covered on the screen, then place it at 3 feet, then 
at 4 feet, and measure the areas as before. In each case how does 
the amount of light falling upon a square inch of the screen compare 
with the whole amount which comes through the hole in the card- 
board? How does the amount on a square inch of the screen compare 
with that on a square inch of the cardboard ? 

82 



Light. 83 

Photometry. — Upon the above law is based the art of 
photometry ; i.e. the comparison of the illuminating power 
of different sources of light. The standard of comparison 
is a sperm candle of the size called ** sixes '' when burning 
120 grains per hour. 

Experiment 62. — Melt a small piece of paraffin and make a grease 
spot about an inch in diameter on a sheet of unglazed white paper. When 
cold, remove all surplus paraffin, then heat the spot with a warm iron to 
get the grease well into the paper. Mount the sheet in a frame and sup- 
port it upon a graduated board (Fig. 56) . Now place a standard candle 
C at one end of the board, a flame L to be measured at the other, and 







ill'iiiiii'iii""iiii"iiii'""iiii"iiiiiiiii"iiiiii niMi mini i^mmmmTTwn iiiiiiiimiiiiiiiiiriiHiiiiiiiiiiiiimiiiimnimiiiiiiiniiiii 

Fig. 56. 

the photometer sheet P between them, so that they will all be at the 
same height and in a straight line. By trial find a position between the 
lights where the grease spot becomes invisible, or least inconspicuous, 
when viewing it in line with the three objects. This will occur only 
when the sheet is equally illuminated upon both sides. Then by apply- 
ing the above law the candle-power of the flame L may be found. 

For example, suppose that when the spot became invisible the dis- 
tance PC was 2 feet and PL was 6 feet ; then the candle-power of L is 
62 ^ 2^, or 9. In other words, L is equivalent to 9 standard candles in 
illuminating power. Try other flames in place of L, 

Nature of Light. — If we place a book in the sunlight, it 
is illuminated — the eye is affected ; it is warmed, as we can 
determine by touching it ; and if the book remains in strong 
sunlight for a long time it may turn yellow — its chemical 
composition is affected or changed. These experiments 



84 Elements of Physics. 

and our experiments with the radiometer indicate that what 
we receive from the sun is some form of energy, and other 
experiments lead us to beheve that it is one and the same 
form whatever the effect. 

All evidence goes to show that light is radiated from 
the sun, or other source, in the form of ether waves or 
vibrations, and that the only difference between those 
which produce light and those which produce heat is their 
difference in wave length and rate of vibration. This is 
called the undulatory theory of light. 

Bodies Classified. — Whenever the temperature of a 
body is so high that the vibrations of its molecules create 
vibrations in the ether capable of affecting the sense 
of sight, the body is said to be himijzoiis. Such bodies are 
said to be in a state of incmidescence. There are a few 
substances which after exposure to light waves become 
luminous without becoming hot, because of the wave 
energy they absorb. This phenomenon is called phospho- 
rescence. If the condition of a body is such that it gives 
no light except that which it reflects from other bodies, it 
is called non-licminoiis. 

Such bodies as glass, air, and others which allow light 
to pass with so little loss that objects can easily be distin- 
guished through them are called transparent. When bodies 
allow light to pass in so small an amount that objects cannot 
be seen distinctly through them, as oiled paper, thin wood, 
etc., they are called translucent bodies. Such bodies as 
hinder the passage of light altogether are called opaqne. 

No body is perfectly transparent or opaque, consequently 
the above is only a classification of degrees. This is evi- 
dent from the fact that objects seen through glass get dim- 



Light. 85 

riier in outline as the thickness of the glass is increased, 
and that every apparently opaque solid becomes translucent 
when made into very thin sheets. 

Rays, Beams, and Pencils of Light. — A single line along 
which light travels is called a i^ay ; it is the path of an ether 
wave. The ether vibrations take place to and fro across the 
ray direction. Rays are of course radial lines extending in 
all directions from the source of light; but at great dis- 
tances, like that from the sun to the earth, those rays which 
strike a small area become nearly parallel. A collection of 
parallel rays constitutes a beam, and a collection of rays 
forming a cone of light constitutes a pencil. The pencil 
may be convergent or divergent. 

Rectilinear Motion and Velocity of Light. — In any 

medium of uniform density light travels in straight lines 
from its source. This fact is of very great importance. 
The velocity of light is about 186,000 miles per second. 
This number was found by observing the eclipses of Jupiter. 
The time of an eclipse can be calculated with great accu- 
racy. It has been found that when the earth is in that part 
of its orbit nearest Jupiter, the eclipse appears to begin 16 
minutes and 36 seconds sooner than when it is in that part 
of its orbit farthest from Jupiter. This shows that it takes 
light 16 minutes and 36 seconds to cross the earth's orbit, 
or approximately 8 minutes and 18 seconds to reach the 
earth from the sun. Dividing the distance from the earth 
to the sun by the time that it takes light to traverse it, we 
have about 186,000 miles per second as the result. For 
distances on the earth the passage of light is considered 
to be instantaneous, because a ray of light would go around 
the earth almost seven times in a single second. 



86 



Elements of Physics. 



Variable Velocity. — We have seen that Hght travels in 
straight lines and the wave front is perpendicular to the 
line of propagation. The velocity varies in different 
media. If light travels less rapidly through medium A 
than through medium B, A is said to be optically denser 
than B. 

Every point in a luminous body is an independent source 
of light waves and emits them in every direction. Hence, 
any body illuminated by a lamp receives light from every 
point of the flame, and when we see any object the eye 
receives rays of light from every point of the object on the 
side toward us. This gives us a kind of picture of the 
object — an image. To illustrate, try the following : — 

Experiment 63. — Cut a hole about an inch square in the bottom of 
a chalk box and paste over it a piece of tinfoil which has a pinhole in 
the middle of it. Cover the top of the box with oiled white paper, then 

hold the tinfoil toward a window, and 
an inverted image will be seen on 
the oiled paper. The lines in Fig. 
57 show why the image is inverted. 
Explain fully. An eclipse of the 
sun may be observed in this man- 
ner. Why? 




Fig. 57. 



Shadows. — By placing a 
book between a lamp flame 
and the wall light is excluded from a space between the 
book and wall. This space is called a shadow. We notice, 
more or less clearly defined, a dark area on the wall the 
same in outline as the book, but this area is not the 
shadow, it is only a section of the shadow, Notice that 



Light. 



87 



this area is made up of two distinct parts — a dark center 
bordered on all sides by a much lighter fringe. The 
dark part is called the umbra, and the lighter part the 
penumbra. 

An explanation of the different conditions possible may 
be had from the study of Fig. 58. First, when the source 
of light is a point, the 
shadow is perfect, hav- 
ing only one part, the 
umbra, whose cross- 
section increases with 
its length. A, in the 
figure. Second, when 
the source of light has 
magnitude, but less 
than the opaque body. 
In this case the shadow 
has two distinct parts 
which increase with 
their length, CB, Fig. 

58. Third, when the source of light has the same mag- 
nitude as the opaque body. Draw the figure and explain. 
Fourth, when the source of light has a magnitude greater 
than the opaque body. Draw the figure and explain. 

Visual Angle. — Since light emanates from all points of 
a luminous body, it is evident that the rays from any two 
points cross each other in all directions and form an infinite 
number of angles which decrease in size as the crossing of 
the rays occurs farther from the body. If two such rays 
from the extremities of the object cross at the eye, the angle 
formed is called the visual angle. The distance between 




Fig. 58. 



88 



Elements of Physics. 



the points of a pair of scissors depends upon the angle 
formed by the handles, and in like manner the size of the 
image formed on the retina of the eye depends upon the 
visual angle. Since the visual angle diminishes as the dis- 
tance from the eye increases, the apparent size of an object 




Fig. 59. 



also diminishes (Fig. 59), at twice the distance the angle 
or apparent size is one-half as great ; at three times 
the distance it is one-third as great ; and so on. When 
this angle is less than one three-hundredth of a degree, 
the object forming it becomes invisible to the unaided 
eye. 

Reflection of Light. — Whenever light waves in passing 
through any medium strike the surface of another medium 
of such a character that only a part of the light enters, the 
other part is turned aside or reflected in harmony with 
the law of reflection, i.e. the angle of incidence equals the 
angle of reflection, and lies in the same plane with it. A 
body which regularly reflects a large amount of light from 
its surface is called a mirror. The smoother the surface 
of the medium against which these waves strike, the better 
the reflection ; hence mirrors are made of solids which 
admit of a very high polish, as glass and some of the 
metals. Mirrors are either plane or curved. Of the 
curved there are two kinds, — the concave and the convex. 



Light. 



89 




Plane Mirrors. — Experiment 64. — Direct a beam of light into a 
darkened room through a small hole, and trace its course by dust 
particles, then place a plane 
mirror on a table so that 
these rays may strike it, as 
in Fig. 60, and note direction 
of the reflected rays. With 
a protractor placed so that 
its 90-degree mark takes the 
direction BP^ determine the 
angles of incidence and re- 
flection. How do they compare ? Set the mirror in other positions, 
and measure again. 

Another method of finding these angles is to let the light pass through 
a hole in a card, C, and fall upon a mirror from which it is reflected to 

a hole in another card, O, Fig. 
61. Then PH being equal to 
PD^ and DA equal to HB^ it is 
easy to prove angle DPA equal 
to angle HPB, and APN^ BPN, 

Rays of light which fall 
upon mirrors may be par- 
allel, convergent, or di- 
vergent ; and all of the 
effects of mirrors on these are explained by reference to 
the law of reflection. By a careful study of Fig. 62 we see 
that in the case of rays reflected by plane mirrors, parallel 
rays are reflected parallel, that converging rays remain 
converging, and that diverging rays remain diverging. 

The image seen in a plane mirror is apparent only, and 
seems to be formed as far behind the mirror as the object 




Fig 01. 



90 



Elements of Physics. 

This is illustrated 



lies in front of it. It is also reversed, 
by Fig. 63. 




Ak — 



Fig. 62. 

AB and AC represent any two rays of light which pass 
from the object A to the plane mirror MN. These rays 

are reflected in the directions 
BB and CB respectively, mak- 
ing, in each case, the angle of 
incidence equal to the angle of 
reflection. 

To an eye ^,t B or D the 
image of A will seem to be at 
A\ as far behind MJV as A is 
in front of it, and on the per- 
pendicular from the object to 
the mirror. 

Concave Mirrors. — Concave mirrors are those whose 
reflecting faces have an inward curve. They reflect all 
rays parallel to the principal axis to a point called the 
principal focus. This focus in the case of a spherical 
mirror is half way from the surface of the mirror to the 
center of curvature (the center of the sphere of whose 
surface the mirror is a part). The best form of concave 
mirror is slightly modified from the spherical, so that if 
rays of light be started from the principal focus they will 
become parallel after being reflected. By an application 





Light. 91 

of this principle, search-lights and head-lights are made to 
produce a great illumination. 

Fig. 64 shows the effect of spherical concave mirrors upon 
parallel rays of light ; that such rays are converged and that 
the principal focus, F, lies between the 

center of curvature, C, and the surface ^ 

of the mirror. To construct the angles e^-J^ 

of incidence we must erect a perpen- ^ 

dicular to the concave surface at the 

r . . 1 / T 1 F^G. 64. 

pomt of mcidence (a perpendicular to 

any spherical surface lies along the radius of the sphere). 

Fig. 65 shows the effect of concave mirrors upon rays di- 
verging from a given point, F, By constructing the angles 
of incidence and reflection, we find that 
the rays diverge less rapidly as re- 
flected than they converged as inci- 
dent rays. From the above we may 
say that the general effect of a concave 
Fig. 65. mirror is to collect rays of light. 

When an object is placed in front of a concave mirror, 
the size and position of the image will depend upon the 
distance of the object from the mirror. There are three 
special cases : — 

First, when the object is beyond the center of curvature. 
In this case the image will be between the center of curva- 
ture and the principal focus, inverted, and smaller than the 
object. Draw a figure to illustrate this. 

Second, when the object is between the center of curva- 
ture and the principal focus. In this case the image will 
be beyond the center of curvature, inverted, and enlarged. 




92 



Elements of Physics. 



Third, when the object is between the principal focus 
and the mirror. In this case the image will be behind 
the mirror, erect, and enlarged. Draw the figure to illus- 
trate this. 

Convex Mirrors. — Convex mirrors are those whose reflect- 
ing surfaces are curved outward. Their general effect is to 
increase the divergence of rays of light ; i.e. parallel rays 
are made divergent, divergent rays are made to diverge more, 
and convergent rays are made to converge less. All images 
are behind the mirror, erect, and smaller than the object. 

Refraction. — Light will pass through several media with- 
out bending if it strikes the surface of each perpendicularly ; 

but if the rays strike the sur- 
face of any medium obliquely 
they are turned aside or re- 
fracted, as shown in Fig. 66. 
The short lines represent 
the wave front, and the long 
line the direction of the ray. 

Experiment 65. — Place a coin in an empty vessel in such a posi- 
tion that a person standing at one side can just see it over the edge of 
the vessel (Fig. 67), then gradually pour water over it, carefully noting 




Fig. 66. 





Fig. 67. 



Fig. 68. 



the apparent movement of the coin. The beam of light is bent at 
Z^, where it leaves the water and takes the direction DE. The coin 
appears to be at C, which lies in ED produced (Fig. 68). 



Light. 



93 



Questions. — i . Account for rivers appearing shallower than they 
really are. 

2. Account for the bent appearance of a stick when thrust into 
water obliquely. 

3. Lay a thick piece of glass over a line in this book and account 
for the appearance of the line. 

Angle of Refraction. — The direction which a ray of 
light takes in passing from one medium into another 
depends upon the relative densities of the media and the 
angle of incidence of the ray. If the incident ray is per- 
pendicular to the bounding surface, there will be no refrac- 
tion. It is of great importance to know what direction a 
refracted ray of hght will take when entering a given 
medium. There are two laws of refraction: (i) in going 
from a rarer to a denser medium light is bent tozvard the 
perpendicular ; and (2) in going from a denser to a rarer 
medium it is bent from the perpendicular. The eye 
which receives refracted rays of light traces them back- 
ward in straight lines, and 
objects are thus made to ^ 

appear where they are not. 

Index of Refraction. — 

The relative refracting 
powers of different sub- 
stances are indicated by 
certain numbers called in- 
dices of refraction. This 
term can be best under- 
stood by a study of Fig. 
69. Suppose a ray of pt 

light, RI^ to be passing fig. 69. 



^ 


T \^ 


\ I 


^-^V 


Ps^ 


-— -~— ^/C 






m 

lull! III! 


fs^-i 



94 



Elements of Physics. 



from air into water. It will be bent at /, and take 
the direction IS'. Now with / as a center, and any con- 
venient radius, draw a circle. Erect P^I perpendicular 
to the surface of the water at /, and from points vS and 
O let fall perpendiculars to P'L From trigonometry we 
learn that line OT is proportional to the sine of the angle 
of incidence, and line SP is proportional to the sine of the 
angle of refraction. Now, if these two lines be measured 
and the length of 6^7^ be divided by that of SP, the 
quotient will be the index of refraction. 



With the two media above mentioned the line OT \s -^-^ 
of the radius 01 and this ratio is the sine of the angle of 
incidence ; and the line SP is -^-^ of the radius and this 
ratio is the sine of the angle of refraction. The -^-^ divided 

by TO gives 1.33, the in- 
■^ dex of refraction for water. 

I The greater the refracting 

I power of the substance, 

j the larger is the index of 

j refraction. An absolute 

^' ^^iV index of a given medium 

is obtained only when the 
^p ^;^-^^i:z=^-^=^^^^^-^-^.=:^^=^i^^=E^;^ light passes from a vacuum 

into the medium, hence the 
^^^ -0^^^^-^^^ =j.-^=£r-^=^ z ^^3^ above method gives only 

relative indices. 
M 
Fig. 70. 

The index of refrac- 
tion for diamond is nearly 2.5 ; for flint glass, nearly 1.6 1 ; 
for crown glass, 1.58 ; for alcohol, 1.37; for the humors of 
the eye, 1.35. For a given medium the index of refrac- 




Light. 95 

tion is a constant quantity. From experiments we learn 
that when rays of Hght are passing from a medium of 
high refractive power into one of low refractive power, 
the refracted rays rapidly approach the surface of the 
rarer medium as the angle of incidence is increased. 
Then there must be an angle of incidence such that the 
angle of refraction will be 90 degrees ; i.e, the refracted 
ray will just graze the surface of the medium. This 
is called the limiting or critical angle {COM^ Fig. 70). 
It is now evident that any incident ray, as OR, which 
makes a larger angle than COM, cannot emerge from the 
medium, hence cannot be refracted. Such a ray is reflected 
within the medium taking the direction OX : this is called 
total internal reflection. Total internal reflection always 
occurs when rays of light in a high refractive medium are 
incident at a greater angle than the critical angle. Trans- 
parent media under such conditions make the best mirrors 
possible. 

Prisms. — Any transparent body having two plane 
surfaces inclined toward each other is a prism. The most 
convenient form is made of glass and has a 
triangular cross-section (Fig. 71). The tri- 
angular pendant from a chandelier or a parlor 
lamp will serve the purpose of experiment 
very well. fig. 71. 

Prisms produce two simultaneous effects upon light 
which passes through them, — refraction and decompo- 
sition. Decomposition is caused by refraction and is 
usually termed dispersion. The refraction is shown by 
Fig. 72, in which a ray of light, AB, is incident upon the 




96 



Elements of Physics. 




prism at B, On entering it is bent in the direction BC, 
where it is again refracted along CD\ and to an eye at 

D, the object at A 
will appear to be 
at F, At both sur- 
faces the light is 
bent toward the base 
^^^- 72- of the prism. 

Dispersion is shown by the following : — 

Experiment 66. — In a thick piece of paper cut a slit an inch long 
and not over J^ of ^'^ i^ch wide. Tack the paper over an opening 
where the sunlight may enter through the sht. If we look at the sht 
from E^ Fig. ^-^^ we shall see the sun beyond. If a prism, P^ be placed 



j^-^" 




horizontally in the path of this light, the light will be refracted upward, 
and if it be caught upon a screen, it will appear as a band of light of 
various colors passing by delicate gradations from violet at the top 
through indigo, blue, green, yellow, and orange to red at the bottom. 

The Solar Spectrum. — This beautiful band is the solar 
spectrum^ and the production of it by the prism is called 
dispersion. It depends upon the fact that rays of different 
colors are refracted in different degrees. A very sensitive 



Light. 97 

thermometer held in the colors of the spectrum shows the 
presence of heat; and it has been found that the tem- 
perature increases from the violet toward the red. It 
has also been found that there is an invisible part of the 
spectrum refracted less than the red which manifests itself 
as heat, and a part more refracted than the violet which 
manifests itself by chemical action. 

Recomposition. — Experiment 67. — Hold a large lens so that it will 
catch all the rays after refraction by the prism in Experiment 66, and 
by holding a paper in their path find the principal focus. It will be 
noticed that a bright spot of white light occurs there. Place two prisms 
together so that the base of one will be opposite the base of the other, 
and notice that the rays which at first passed through as a spectrum 
are now passing through as white light. 

This recombining of light after it has been separated by 
the prism is termed recomposition or syiitJiesis of light. 

The Spectroscope is an instrument used to examine the 
spectra of different substances. It consists of one or more 
prisms for producing the spectrum, and a telescope for 
examining it. The light is admitted to the prism through 
a very narrow slit, because when it comes through a large 
hole the colors overlap. This instrument has proved to be 
one of the most valuable aids to modern science, because 
it affords a most delicate means of chemical analysis. By 
analvTing the light of different known substances and com- 
paring it with the dispersed light of the sun we are able to 
determine with certainty that sodium, calcium, copper, zinc, 
magnesium, hydrogen, and other substances exist there. 

The Rainbow. — Drops of rain decompose sunlight in 
the same manner as a prism, and in this way produce the 



98 



Elements of Physics. 



rainbow. There are usually two bows formed ; an inner 
or p^'imary and an outer or secondary bow. The primary 
bow consists of concentric arches of the colors of the 




Fig. 74. 



spectrum with red on the outside ; the secondary bow has 
the same colors in reverse order, the violet being on the 
outside. An understanding of the formation of these bows 



Light. 



99 



may be had by a study of Fig. 74. 55, S'S^ are rays of 
sunlight. An observer at E will receive red light from 
every raindrop situated 42"^ from the line AC, drawn 
through the sun and the eye, and vto/et from all drops 
40"^ from the same line. Since the drops are spheres, they 
send light in all directions, hence all those in a circle 
about C and 42° distant will send red to the eye and form 
a red arch, while those at 40° will send violet. The other 
colors will arrange themselves in regular order between 
these two colors. 

In explaining the primary bow we traced the rays which 
fall upon top of the drops of water, but to explain the 
secondary bow we trace the rays which fall upon their 
under sides. In order that such rays may reach the eye 
the drops must be about 54° from C for the violet and 51"^ 
for the red. This bow is not so bright as the primary on 
account of the loss of light due to the two reflections which 
take place inside the drops. 




12 3 4 

Fig. 7S. 

Lenses. — Any transparent body bounded by two curved 
surfaces, or by one curved and one plane surface, is a lens. 
With respect to their effect upon light they are of two 
kinds : convergent and divergent. Of the convergent 
lenses there are: (i) double convex, (2) plano-convex, 
(3) meniscus or concave meniscus ; and of the divergent 
L.ofC. 



lOO 



Elements of Physics. 



there are: (4) double-concave, (5) plano-concave, (6) con- 
cavo-convex, Fig. 75. The converging lenses are thicker 
in the middle than at the edges, and the diverging lenses 
are thinner in the middle than at the edges. 

Experiment 68. — Hold an ordinary burning glass or spectacle lens 
in the sunlight, and notice the direction of the rays after they pass 
through the lens. By placing an object in the path of these rays, find 
where they come to a point. This point is called \h^ principal focus, and 
its distance from the lens is called \\\^ focal length of the lens. Obtain 
another lens and find its focal length, then place the two together, and 
you will find that the focal length of the combination is less than that 
of either one alone. Look at the letters of your book through each 
lens separately, then through both together, keeping in mind their rela- 
tive focal lengths, and verify the following : the shorter the focal length 
of a lens, the greater its magnifying power. 




Fig. 76. 

Foci. — The focal length of a lens depends upon its 
curvature and the index of refraction of the material of 
which it is composed'. If both surfaces are equally curved, 
and if the lens is made of glass whose index is 1.5, the 
principal focus will be at the center of curvature. If rays 
of light from a point upon one side of a lens pass through 
the lens and are brought together at a point upon the other 
side, the two points are called conjugate foci. The princi- 
pal axis of a lens is a line passing through its centers of 



Light. 



lOI 



curvature, AB, Fig. 75. The point at which rays parallel 
to this axis meet after passing through the lens, as in 
Fig. 76, is called the principal focus of the lens. 

Experiment 69. —Take a lens that is thinner in tlie middle than at 
its edges and note its effect upon rays of light, in the manner indicated 
in the above experiment. 

We may better understand the effect of lenses upon 
rays of light by regarding these lenses as 
formed of two approximate prisms — their 
bases being together in the convex lens, 
as in Fig. 77. ,4, ^ 




Fig. jj. 



Formation of Images by Convex Lenses. — Ex- 
periment 70. — Hold a convex lens in front of a 
window and hold a paper behind it at its principal 
focus. When the distances are just right, a small inverted image of 
the window will be seen upon the paper. 

Account for the view in the - finder '' of a little hand camera. 




Fig. 78. 



Represent the lens in the above experiment by Z, Fig. 
78, and the window by the arrow, NS. Two rays of light 
passing from iV through L will be refracted and meet at X, 
while the rays from 5 will be refracted and meet at Y. 
Then X is the image of point .V, and Y is the image of 
point S. Rays from all other points will be collected at 



I02 Elements of Physics. 

corresponding points between X and Y and the whole 
will form a complete inverted image of the arrow NS, 

The size and position of the image will depend upon the 
distance of the object from the lens. The following cases 
may be considered : ist, when the object is twice the focal 
length from the lens ; 2d, when more than twice the focal 
length ; 3d, when less than twice the focal length, but more 
than once its length ; 4th, when less than the focal length. 
Illustrate these cases by drawings.. 

Images of Concave Lenses are on the same side of the 
lens as the object, smaller and erect. 

Optical Instruments. — Upon the principles of reflection 
and refraction is based the construction of the microscope, 
telescope, stereoscope, and many other optical instruments. 




Fig. 79. 



The Microscope. — There are two kinds. The simple 
microscope consists of one convex lens so placed that the 
light from an object at less than the focal length appears 
to come from a much larger object (Fig. 79). The com- 
pound microscope consists of two or more lenses so arranged 



Light. 



103 



that each lens toward the eye magnifies the image formed 
by the one in front of it. Its action is illustrated by Fig. 80. 
The objective^ O, forms a real image, A^B\ of an object 
AB ; and the eyepiece, Ey magnifies this image so that it 




appears to be the size of XY. From this we can see the 
advantage of the compound microscope over the simple. 
For if the objective magnifies 10 times and the eyepiece 
10 times we have a magnifying power of 100 times. 
Then if there are several lenses in the objective and their 
focal lengths are small, the result will be a very powerful 
instrument- — the product of their respective powers. * 

Telescopes are used for viewing objects that are far off. 
They are called terrestrial or astronomical according as 




Fig. 81. 



they are used to view bodies on the earth or in the 
heavens — the difference being that the terrestrial gives 
an upright image while the astronomical gives an inverted 
image. The erect position of the image as seen in the 
terrestrial telescope is produced by the use of two extra 



I04 



Elements of Physics. 



lenses. Telescopes are called refracting or reflecting 
according as the objective is a convex lens or a concave 
mirror. The power of a telescope equals the focal length 
of the objective divided by that of the eyepiece. Fig. 8i 
represents the action of the refracting telescope. For a 
more detailed description of microscopes and telescopes, 
see Ganot's '^ Physics." 

The Human Eye. — This most wonderful optical instru- 
ment is a nearly spherical ball composed of three coats. 
The inner coat, or retina (9), (Fig. 82), serves as a screen 




Fig. 82. 

upon which an inverted image of all objects in the line of 
vision is formed. Rays of light from an external object in 
order to enter the eye must pass through the cornea (4), 
and the aqueous humor (6), to the crystalline lens (7), 
which focuses the image, then through the vitreous 
humor (8), to the retina (9), where vibrations are set up 
in the nerve filaments and the sensation of sight produced. 



Light. 105 

Color. — Dr. Young (1801-2) advanced a theory that 
these nerve filaments are capable of only three color sen- 
sations, — red, green, and violet; and that when combined 
with proper intensities they produce the different sensa- 
tions of color; and that when excited simultaneously with 
proper intensities they produce white light. When any 
person is deficient in respect to one of these sets of nerve 
fibres, he is said to be color-blind. 

Short and Long Sight. — If the globe of the eye is too 
long from front to back, myopia (short-sightedness) is the 
result; i.e. images of all but near objects are formed before 
the rays reach the retina. The remedy lies in the use of 




(2) Far-sighted Eye. (I) Normal Eye. (3) Near-sighted Eye, 

Fig. 83. 

diverging lenses. If the globe is too short in this direc- 
tion, the rays strike the retina before an image is formed ; 
i.e, the image is formed back of the retina unless the 
object is far away, and Jiypennetropia (long-sightedness) is 
the result. The remedy lies in the use of converging lenses. 

The Camera is an instrument working on the same 
principle as the eye, except that the focus for objects at 
different distances is formed by changing the position of 
the plate holder instead of by automatic variation of the 
curvature of the lens as in the eye. Illustrate by Experi- 
ment 63, using a convex lens at the hole in the box. 



io6 Elements of Physics. 

The Stereopticon is extensively used in the lecture room 
for producing very large images of small transparent 
pictures, called slides. It is similar in its action to the eye 
except that the order of the lenses and the direction of 
the rays are exactly reversed. See Appleton's *' School 
Physics," and, if possible, study the instrument. 

The Heliograph is an instrument for producing a series 
of signals by flashes of light by reflection. In this way 
messages have been sent over very long distances. The 
heliograph was used very successfully in 1899 in the Anglo- 
African War between the English and the Boers. 

For a description of a stereoscope see any good 
encyclopedia. 

Questions for Review. — i . What relation exists between heat and 
light? 

2. How may non-luminous bodies be made to become luminous? 

3. What are transparent bodies? Translucent bodies? Opaque 
bodies ? 

4. How can you prove that light goes in straight lines? 

5. Why are images formed through small apertures inverted? 

6. On what does the size and brightness of an image depend? 

7. What is the velocity of light? How and by whom was it first 
determined? 

8. Describe reflection and state the law. 

9. What are incident rays ? 

10. Why is a room with light walls lighter than one with dark walls, 
even when the same amount of light comes into the room ? 

1 1 . What is a mirror ? 



Light. 107 



12. Name the kinds of mirrors and tell their effect upon light rays. 

13. What is the axis of a mirror? The principal focus? 

14. What is refraction? \Vhen is light refracted? How? 

15. What is the index of refraction ? How found? 

16. Why are fish hard to kill by shooting? 

17. Do we ever see the sun before it rises? W^hy? 

18. Why do diamonds sparkle? 

19. Upon what principles may imitation stones be made? 

20. Explain total reflection and the critical angle. 

21. What is a prism? What effects does it have on light? How? 

22. Explain the use of the spectroscope. 

23. When and why are images by lenses inverted? 

24. On what does the color of a body depend ? 

25. When is a substance black? When white? 

26. Is black or white a color? 

27. Why are white garments seasonable in summer? 

28. What are the parts of the eye? Their uses? 

29. What is the use of convex spectacles lenses? 

30. What disease of the eye needs concave lenses? 

31. Why not read while lying on the back? 

32. Why not sleep with a lighted lamp in the room? 

33. Why are electric lights better than kerosene lights when they 
have the same candle-power? 

34. Why is it injurious to read on a moving train? 



io8 Elements of Physics. 

35. Which is better for the eye, direct or reflected hght? Why? 

36. What is a microscope? What determines its power? 

37. Why are high mountains better for astronomical work than low 
valleys? 

38. What is the difference between a microscope and a telescope? 

39. What is photometry? 

40. What is the rainbow? Why is it circular? 

41. The candle-power of two flames are as 10 to i ; how far from 
each must a paper be placed to be equally illuminated by both ? 



CHAPTER VII. 

MAGNETISM. 

Magnets. — The word '' magnet " is derived from the Greek 
word which was applied to a black brittle ore of iron found 
near Magnesia, an ancient city of Asia Minor. This ore 
was found by the ancients to possess the property of 
attracting small bits of iron or steel. It has since been 
found to attract nickel and cobalt. This same ore is found 
in other parts of the earth and is called lodestone, meaning 
'' leading " stone, because it points north and south if poised 
so that it is free to turn. By the use of the magnet our 
sailors are led across the ocean, and surveyors are guided 
in their work. A piece of the ore is called a natitral mag- 
7iet. A bar of steel may be made a permanent magnet by 
stroking it several times in one direction with this mineral. 
Steel retains magnetism longer than soft iron and will not 
break so easily as lodestone ; hence a bar of steel is gen- 
erally used in place of the lodestone and is called an mii- 
ficial magnet. It is advisable to use steel magnets for the 
following experiments ; and if one is at hand, others can 
be made by treating bars of steel with this, stroking them 
in one direction with only one end of the magnet. 

Experiment 71. — Sprinkle iron filings or small tacks over a bar 
magnet. Pick up the magnet, holding it at the middle, and notice that 
the particles at the' ends of the magnet are held while those at the mid- 
dle are not. This shows that the attractive power of a magnet is near 

109 



no Elements of Physics. 

the ends. These points near the ends are called poles, and every mag- 
net, however small, has two poles. One is called the north pole, and the 
other the south pole. 

Experiment 72. — Suspend a bar magnet so that it will be free to 
turn. When it becomes still, bring the end of another near it. Reverse 
the second magnet and note the result. 

Experiment 73. — Place both ends of two bar magnets in iron filings, 
then bring the poles together alternately. Note that when certain 
poles are brought together they tend to unite their loads, while certain 
poles tend to lessen each other's loads ; i.e. they will not hold a united 
load. Note carefully the poles which hold a united load and those 
which do not. 

Law of Magnetic Attraction. — By applying a bar mag- 
net to a magnetic needle, as found in an ordinary pocket 
compass, we may determine which end of the needle is the 
north pole and which is the south. The north pole is 
marked plus, and the south minus. From the preceding 
experiments we learn that the law of magnetic attraction 
is : Like poles repel each otlier^ and ttnlike poles attract each 
other. 

Care of Magnets. — In order that magnets may keep 
their power, it is well to observe the following rules : 

1. Always keep the armature on a horseshoe magnet. 

2. Bar magnets should be laid in pairs with their opposite 
poles together, or with bars of soft iron across their ends 
as keepers. 3. Do not leave the south pole pointing north. 
4. Never allow a magnet of any kind to receive rough 
treatment. 5. Never heat a magnet. 

Magnetic Field. — Experiment 74. — Place a bar magnet horizontally 
and cover it with a sheet of paper or cardboard, then sprinkle iron filings 



Magnetism. 



Ill 




Fig. 84. 



upon the paper. The position of th6 magnet will readily be seen. Tap 
the paper gently and note how the filings arrange themselves along 
definite radial lines, coming out of 
one pole and by graceful curves en- 
tering into the other, as in Fig. 84. 
Note that each of the filings lies 
along a line of magnetic force. 
These lines mark the adjacent mag- 
netic field and are called lines of 
magnetic force. Any magnetizable 
substance brought within this field is acted upon by a pecuHar mag- 
netic force which may be called ether stress. 

Experiment 75. — Place a horseshoe magnet under the paper with 
its poles vertical and note the shape of its field and its apparently greater 
strength (Fig. 85). 

Magnetic Induction.— Experiment "jd. — With 
a strong bar magnet pick up a tack and add other 
tacks to this one as long as they will hold. The 
first tack will be found to be a magnet. Now 
take a small unmagnetized nail and hold it near 
the magnet, but not touching it, then let the nail touch a tack or iron 
filing, and the nail will be found to possess m.agnetic force. This 
process by which magnets may induce magnetism in other bodies with- 
out touching them is called 7nagnetic indiiction. When the magnet is 
removed, the other body apparently loses its magnetism. 

Nature of Magnetism. — The precise nature of magnetism 
is a subject not thoroughly understood, yet it is not more 
puzzling than gravitation, cohesion, or radiation. Mag- 
netism has been spoken of as an ether stress. The phe- 
nomena of attraction and repulsion tempt us to investigate 
the cause of this stress. That ether is the medium through 




Fig. 85. 



1 1 2 Elements of Physics. 

which this force operates is suggested by the action of 
magnets when not in contact with the bodies which they 
attract or repel, even in a vacuum. The fact that a mag- 
net exerts an influence through glass, which is a non- 
conductor and a non-magnetizable substance, shows that 
there is a medium among the molecules which renders 
such action possible. This ether stress, as we have seen, 
extends indefinitely in all directions around a magnet, and 
its intensity diminishes as the distance increases. (See 
law of gravitation, page 14.) Any magnetizable substance 
coming within this field or region of stress has its mole- 
cules turned into new positions, hence it becomes a 
magnet. Such conditions and results were illustrated in 
Experiment 76. 

Experiment ^^ . — Place a bar magnet in a shallow dish and cover 
it with water about an inch deep, then sprinkle the water with fine iron 
filings. Note the arrangement of the filings. Bring another magnet 
into the field above the water, reversing the poles ; the filings will 
rearrange themselves. 

Experiment 78. — Magnetize a piece of steel wire a foot long by 
contact with a magnet, then test it for polarization. Break it at its 
middle point and test the ends of both pieces as before. Break these 
halves at their middle points and test again. Continue the breaking 
and testing to any Umit practicable and notice that polarization still 
exists. 

The supposition is that if the breaking could be continued to the 
molecules, each would be found to be a magnet. 

Experiment 79. — Fill a glass tube about half an inch in diameter 
and six inches long with steel filings. Using a bar magnet, treat the 
tube and contents as you would treat a steel bar which you wish to 
magnetize. Bring a compass needle near one end of the tube and 



Magnetism. 113 

note the effect on the compass ; change the compass to a position near 
the other end of the tube and observe. Shake the tube thoroughly and 
test again, and it will be found that there is no evidence of polarity 
in the tube. This shows that magnetism is due to a certain arrange- 
ment of the molecules, and that the only difference between a magnet 
and an unmagnetized piece of steel is that the molecules in the magnet 
are arranged in a certain definite order, and that those in the unmag- 
netized one are in disorder. Continuing this thought, we may say that 
the particles of steel are not made magnets, but that they are simply 
rearranged so that they do not entirely neutralize each other. They 
are ahvays magnets. 

The Magnetic Needle. — A magnetic needle is a bar 
magnet in the form of a slender piece of steel, carefully 
supported at its centre so that it may move freely in any 
direction. To make a needle that will answer for most 
experiments, take a piece of a watch spring five or six 
inches long and straighten it, then 

hold the middle in a flame to soften ^ 

it. Bend it as nearly double as pos- 
sible without breaking, then bend 
it back in line, as represented in 
Fig. 86. Magnetize it, then wind a ^_ 



nm 



thread around the short bend that is -pic. 86. 

left, and balance it on the end of a 

needle stuck in a cork. A magnetic needle as above 
described, balanced on a fine point at the centre of and 
just above a graduated circular scale, and enclosed in a 
case, is called a compass. 

Declination of the Needle. — The mariner's compass has 
been in use for nearly three thousand years ; that it does 
not always indicate a true north and south direction has 



1 1 4 Elements of Physics. 

long been known. This deviation from the meridian is 
known as the declination of the needle, and imaginary 
lines upon the earth along which there is no declination 
are called lines of no variation. This declination is sub- 
ject to changes through long periods of years. For in- 
stance, in London, where observations have been made 
extending over a very long period, the magnetic declina- 
tion was found in 1580 to be 11° 15' east. In 1657 this 
was reduced to zero, and the compass needle in that locality 
pointed to the true north. 

TJiis variation may be calculated by moving the Hnes of 
known measurement one degree west for every twelve 
years. A practical method is as follows : Set two stakes 
some distance apart and in line with the north star, and 
join them with a string. This string will be on the geo- 
graphical meridian. Place over the string a long magnetic 
needle. The angle made by the needle and string will be 
the angle of declination. This will be sufficiently accurate 
for many purposes ; but if greater accuracy is required, 
allowance must be made for the fact that the north star 
is not always exactly over the north pole, but describes 
around the pole a circle whose diameter is about four 
degrees. 

Inclination of the Needle. — If the position of a magnetic 
needle in this latitude be studied carefully, it will be found 
to be not in a horizontal Hne, but dipping down toward the 
north. In the southern hemisphere the dip will be toward 
the south. This variation is known as the iitclinatioji of 
the needle, and is apparent at all places on the earth, ex- 
cept on a circle known as the magnetic equator. This is 
because the earth is a magnet, and all the properties of 



Magnetism. 1 1 5 

magnets previously studied are possessed by the earth. 
It is thought, however, that the magnetism of the earth may 
be caused by its being unequally heated. It is known that 
a magnetizable substance becomes a magnet when heated 
only on one side or at one end. The earth has one side 
toward the sun and heated, while the other side is away 
from the sun and cold ; this causes lines of magnet force 
to be set up around it. For the theory of the earth's 
magnetism, see S. P. Thompson's '^ Elementary Lessons in 
Electricity and Magnetism," page 145 et seq. The north 
magnetic pole of the earth is located in the northern part 
of British America, a little north and west of the entrance 
to Hudson Bay. 

Questions for Review. — i. What is a natural magnet? 

2. What are poles of a magnet? How are they determined? 

3. What is the law of attraction and repulsion between the poles 
of magnets ? 

4. What is magnetic induction? 

5 . What care should be taken of magnets ? 

6. What are lines of force? 

7. What is the difference between a steel magnet and any ordi- 
nary piece of steel ? 

8. Which makes the better magnet, steel or iron? Why? 

9. What is a magnetic needle? What is its use? 

10. What is meant by the declination of the needle? How is it 
found ? 

1 1. How do we know that the earth is a mas^net? 



CHAPTER VIII. 

ELECTRO-DYNAMICS . 

Electricity. ■ — In the preceding chapter we studied a 
force called magnetism, here we take up another force 
which acts in many ways like the magnetic force, though 
it is not so selective in the substances affected. The mag- 
netic force influenced iron and a few other substances, and 
was possessed by very few substances, while the force we 
are now to consider can be possessed by many substances 
and affects nearly all substances to some degree. It was 
known to the ancients that amber, when rubbed with some 
soft material, possesses the power of attracting very light 
bodies. It has since been discovered that many other sub- 
stances exhibit the same property. The Greek name for 
amber is electron, hence the name '' electricity " has been ap- 
plied to this property, and bodies which manifest this force 
are said to be electrified or charged with electricity. 

Experiment 8o. — Rub briskly with a piece of catskin a hard rubber 
rod, and hold it near two pith balls suspended by small silk threads. 
The balls and threads are at first attracted by the rod, but after a 
time they are repelled. Try the rod on bits of paper, cork, and other 
light objects. Now use a glass rod instead of the rubber and a piece 
of silk or flannel instead of the skin. Try a rubber comb, or a stick 
of sealing wax, rubbed with flannel. 

From the above we learn that a rubber rod, rubber comb, 
stick of sealing wax, or glass rod, when rubbed with a suit- 

ii6 



Electro-Dynamics. 



117 



able material attracts small bits of paper, pith balls, saw- 
dust, strings, etc., and that these latter are under the 
influence of the electrified bodies when they are not in 
contact as well as when they are in contact with them. 
We also learn that any of the electrified articles repel 
other objects at times and thus influence them when not in 
contact with them. 

Experiment 81. — Suspend a 
glass tube, closed at both ends, so 
that it will move freely (Fig 87). 
Electrify this rod and a similar one 
by rubbing them with silk. Place 
the rod in the wire loop and hold 
the other near it. What happens ? 
Now electrify the rubber rod and 
hold it near the end of the glass 
rod. What happens? 

Experiment 82. — Electrify the 
pith balls with the glass rod until 
it repels them, then hold the silk close to them. Try the same with the 
catskin after electrifying the balls with the rubber rod. Compare resuUs. 




Fjg. 87. 



Positive and Negative Electricity. — These two experi- 
ments show that there are two kinds of electricity and that 
both are generated at the same time. That generated by 
the glass rod rubbed with silk is called positive and that 
generated by the rubber rod rubbed with flannel is called 
negative. When two bodies are differently electrified, i.e. 
one positive and the other negative, they both become 
unelectrified if their charges are added together. These 
charges neutralize each other like two equal positive and 
negative quantities. Hence the terms '' positive " and 
"negative" for the two kinds of electricity. 



ii8 



Elements of Physics. 



Experiment 83. — Fasten a pointed wire to an electric plate machine 
and hold a candle flame near it. The flame will be blown aside. 
Moisten the finger and hold it near the point of the wire, and a coo] 
breeze will be felt. 




Fig. 88, 



Experiment 84. — Let some one stand on an insulated stool and 
hold the positive pole of the electric machine. No electricity will be 
felt until he touches some other person. The electricity from the 
machine is stored up in his body, and when he is touched it dis- 
charges ; i.e. the charges of the two persons neutralize each other. 

Potentials. — When neighboring bodies differ in such 
a way that an electrical exchange tends to take place 



Electro-Dynamics. 1 1 9 

between them, they are said to be at different electric 
potentials. If two clouds, or the earth and a cloud, differ 
sufficiently in potential they will be connected electrically, 
producing a flash of Ughtning. The discharge is always 
from a body of high potential to one of low potential, i.e. 
from a positively charged body to a negatively charged 
body ; and if the bodies are insulated, the passage of the 
charge depends upon their relative potentials. If their 
difference in potential is great, the charge is proportion- 
ally great. 

Conductors and Insulators. — When electricity passes 
along a body without producing a flash, that body is said to 
conduct the charge because of the small resistance it offers 
to the electricity. If a body is surrounded by such bodies 
as glass, air, paper, rubber, etc., which do not allow electri- 
city to pass freely over them, it is said to be insulated. The 
bodies surrounding it are called insulators, or non-conduc- 
tors. Under proper conditions, however, all bodies con- 
duct electricity. 

Lightning. — Lightning is an electrical phenomenon of 
exceedingly high tension, and is caused by the rapid ac- 
cumulation of energy due to the friction of the clouds and 
wind or to the condensation which takes place at too high 
a rate for the energy to be diffused by ordinary means. 
The frequent formation of large hailstones during a 
thunder shower shows that this condensation is exceedingly 
rapid, and because it is so rapid an enormous amount of 
heat is generated in the surrounding atmosphere. When 
the clouds are high, the lightning passes between them, 
but when they are low, it passes between them and the 
earth. The flashes pass in a wavy line rather than a zig- 



I 20 Elements of Physics. 

zag line, as has been supposed. That they represent an 
enormous amount of energy is seen from their destructive 
effects. 

It has long been the custom to protect buildings from 
lightning by attaching to the outside metallic rods, with 
points and branches extending above the highest points of 
the building. The lower end of each rod is placed deep in 
the moist ground so as to convey any discharge to the 
earth. Such rods are useful, though buildings are some- 
times struck even when '' protected " in the most approved 
manner ; yet it is very seldom that persons in such building 
are injured. Lightning rods are provided with points 
because electricity passes from a sharp point into the air 
with a silent discharge. A spherical body retains a charge 
given to it while one provided with points is discharged 
almost instantly. In like manner, if a charged body has a 
pointed conductor near it, the electricity will be discharged 
into the point without noise or flash. 

Experiment 85. — Coat a large wide-mouthed bottle within and 
without with tinfoil about two-thirds of the way from the bottom. 
Through a wooden cover closing the mouth pass a small 
metal rod which terminates above in a ball (Why?), and 
from which hangs a chain in contact with the inner lining 
of the jar. Such an apparatus is called an electrical accu- 
mulator, a condenser, or a Leyden jar. Hold the ball on 
the jar to one pole of the electrical machine for some time, 
then remove it, and with an insulated rod connect the ball 
with the outer coat. What happens? 

To make a discharger for the Leyden jar, take a small 
bottle, push a stout brass wire through the cork (Fig. 90), and solder a 
metal ball on each end of the wire. 




Electro-Dynamics. 



121 



The Electroscope is an instrument used to detect the 
presence of electricity in a body and to determine its kind. 
It consists usually of two strips of 
goldfoil, A and B, Fig. 91, sus- 
pended from a brass rod within a 
glass jar. To the upper end of the 
rod is attached a metal disk. If 
an unelectrified body is brought 
near the disk, nothing happens ; 
but if an electrified body is brought 
near, the strips of goldfoil diverge, 
showing the presence of electricity. 
If the electroscope is charged and 
some body similarly charged be 

brought near it, the leaves will diverge farther ; but if an 
uncharged body or one charged oppositely be brought 
near it, the strips will collapse, indicating a discharge. 




Fig. 90. 



Induction. — When experimenting with the electroscope, 
it was found to be affected before an electrified body 
touched it. In like manner, when any in- 
sulated conductor is held in the field of an 
electrified body without touching it, the lines 
of electric force acting upon the uncharged 
body produce in it electricity, and attract the 
electricity of its opposite kind to the nearest 
part of the uncharged body, repelling its own 
kind to the remotest part. This is called 
charging a body by indtcction, and the induced 
charge becomes as great as the charge in- 
ducing it. The body inducing the charge, however, does 
not lose its electricity as it would if placed in contact. 




Fig. 91. 



122 Elements of Physics. 

If any space is completely surrounded by a conducting 
shell, it is shielded from all electrical influences from 
without. By setting a screen made of common wire gauze . 
over the electroscope, both resting upon a metal base, the 
latter may be so protected that upon sending sparks from 
the electric machine through the wire, the gold strips will 
not be affected in the least. If the screen and electro- 
scope rest upon a non-conductor, the strips are affected at 
once. A powder house entirely inclosed in sheet iron, the 
floor included, would be safe from lightning. 

Electrophorus. — Experiment 86. — Into a shallow metal disk pour 
melted sealing wax, making the surface as smooth and level as possible. 

To the center of a somewhat smaller 
metal disk attach a glass or rubber 
handle. Avoid sharp edges on the 
disk. Stroke the wax several times 
with a catskin. (What kind of a 
charge has it ?) Place the disk upon 
the excited wax, and it will be im- 
mediately charged by induction, 
Fig. 92. the upper surface being negatively 

charged, and the lower surface posi- 
tively charged. Why ? Touch the disk with the finger so as to remove 
the negative charge (Fig. 92), then Hft the disk, and it will be found to 
have a strong positive charge. This apparatus was invented by Volta 
in 1775, and is called an electrophorus. 

Various methods have been adopted for generating electricity con- 
tinuously and rapidly from the electrophorus. A well-known generator 
built upon this principle is the Toepler-Holz machine (Fig. 88). On 
the back of a stationary glass plate are pasted two pieces of paper which 
act as inductors ; on a revolving glass plate, in front of the stationary 




Electro-Dynamics. 



123 



one, are pasted tin-foil carriers with a flat-metal button on each to serve 
as contact. As the carriers are about to leave the inductors, the two 
on the same diameter are touched by wire brushes fixed to the stationary 
diagonal rod which crosses the moving plate. The repelled charges on 
the carriers are thus simultaneously removed. 

Current Electricity. — Electricity may be generated in 
several ways. In the preceding experiments we generated 
electricity by friction and by induction, but now we are to 
study electricity as generated by means of a battery, 
dynamo, thermopile, or some form of an electro-magnetic 
machine, and as a current doing work. The two kinds are 
identical, differing only in the mode of production. 

Experiment 87. — Put into a glass vessel of convenient size a mix- 
ture of sulphuric acid and water, one to ten parts respectively. To 
one end of a strip of copper and 
to one end of a strip of zinc 
fasten copper wires. Place the 
strips in the fluid so that they 
will not touch each other (Fig. 
93). Notice that small bubbles 
of gas rise from the zinc and that 
none rise from the copper. Con- 
nect the free ends of the wires 
and note that the bubbles now 
rise from the copper. These 

bubbles are hydrogen gas formed by the chemical union of the zinc 
and the sulphuric acid. This chemical union produces the electric 
current, and the circuit is known as the Voltaic or Galvanic circuit. 

Voltaic or Galvanic Cell. — Such a combination as is de- 
scribed in Exp. 87 is called a Voltaic cell. The current 
passes from the zinc through the liquid to the copper, 




Fig. 93, 



124 Elements of Physics. 

thence through the outside wire and back to the zinc. As 
soon as the circuit is broken the current ceases and the 
chemical action also ceases. This suggests that the electric 
current may be due to the chemical action and that the 
two phenomena are dependent upon each other. 

Local Action. — Ordinary commercial zinc contains im- 
purities such as iron, carbon, etc. Almost any two unlike 
metals placed in a solution of acid form a Galvanic cell. 
When a cell like that described in Exp. 87 is used and the zinc 
is impure, currents flow from the zinc to the bits of iron, etc., 
in the impure zinc as well as from the zinc strip to the 
copper strip. In this way a great deal of the zinc which is 
consumed goes to furnish these local currents between the 
bits of iron and adjoining zinc, and only a part of the con- 
sumed zinc furnishes the current which goes along the 
wire outside the cell to do useful work. This waste of zinc 
in local action may be avoided by rubbing mercury on 
the zinc plate, i.e. by amalgamating it. Mercury dissolves 
zinc and brings to the surface of the strip a layer of pure 
zinc which covers the impurities and furnishes a pure 
metal for the acid to act upon. Pure zinc is not acted on 
very rapidly by acid, and all that is consumed furnishes 
current to do useful work outside the cell. 

Polarization. — When the zinc of a cell like that of Exp. 86 
is amalgamated, bubbles of hydrogen rise only from the cop- 
per strip. As more and more bubbles collect on the copper 
strip, the current grows weaker, and when the copper is cov- 
ered by this film of hydrogen, the cell is said to be polarized. 

The weakening of the current by the film of hydrogen is 
due to two facts : first, that hydrogen is a poor conductor of 
electricity ; and second, that it tends to produce chemical 



Electro-Dynamics. 



125 



action at the surface of the copper and set up a counter 
current. 

Varieties of Cells and Batteries. — The kind of cell to be 
employed in producing a current of electricity is de- 
termined by the work to be accomplished. If a current is 
needed for a short time only, what is known as a single- 
fluid cell may be employed, but if the current is to act 
through a considerable time and no great current strength 
is needed, a do iib le-fl? n d cqW is generally used and is known 
as a constant battery. These constant batteries obviate 
difficulties of polarization by placing the inactive metal 
in some liquid of such a character that hydrogen will not 
accumulate upon the plate. 

Daniell Cell. — The oldest and one of the best of the 
constant batteries is a cell invented by Daniell in 1836 
(Fig. 94.) A glass or porcelain vessel 
contains a solution of copper sulphate 
(blue vitriol) in which is immersed an 
open cylinder, C. At the upper por- 
tion of this cylinder is a perforated 
^copper pocket, in which crystals of 
copper sulphate are placed to keep 
the solution saturated. Inside this 
copper cylinder is a porous jar of un- 
glazed earthenware, and in this jar is 
the rod of zinc, Z, immersed in dilute 
sulphuric acid. The porous jar will 
not allow the fluids to mix rapidly, but 
soon becomes so well saturated that it offers very little 
resistance to the molecular action of the fluids and the 
resulting electric cu'rrent. 




Fig. 94. 



126 



Elements of Physics. 



The economy of this cell may be seen by a study of the 
following : The hydrogen which results from the action of 
the acid on the zinc is liberated on the copper plate, but 
at the same instant it combines with the copper sulphate, 
forming sulphuric acid and releasing rr etallic copper which 
is deposited on the copper plate. In this way copper sul- 
phate is used up, but being replaced from the crystals in 
the pocket, the solution is kept at about the same strength. 
The sulphuric acid produced penetrates the porous jar and 
replaces the acid used by the action on the zinc. These 
conditions keep the battery constant as long as copper 
sulphate remains in the pocket provided for it. 

The Gravity Cell (Fig. 95) is simply a modification of 
the Daniell cell. There is no 
porous jar, the liquids being kept 
separated by their difference in 
specific gravity, copper sulphate 
being heavier than zinc sulphate. 
Gravity cells are used in operating 
the telegraph and are especially 
good upon closed circuits. 

The Gjwe and the Bicnsen are 
other forms of double-fluid cells. 




Fig. 95. 



Bichromate Cell. — The simplest 
form of single-fluid cell is known 
as the bichromate cell. It con- 
sists of a zinc plate between two carbon plates suspended 
in a solution of bichromate of potash sHghtly acidulated 
with sulphuric acid. 

The Grenet Cell (Fig. 96) is a common form of the bi- 
chromate cell, and produces good results whenever a strong 



Electro-Dynamics. 



127 




current is needed for a short time. The zinc, Z, should be 
Ufted out of the fluid when the cell is not in use. The 
objection to this cell is that the fluid travels 
up the carbon plates and attacks the con- 
nections. The chromic acid formed in this 
cell oxidizes the hydrogen and forms water, 
thus preventing polarization. 

Dip Battery. — A good working battery 
for laboratory use is a dip battery. Any 
number of cells may be managed an this 
manner, as it is so constructed that all the 
plates may be raised out of the liquid when 
not in use; or they may be raised for a brief 
interval at any time to restore the battery. 

Leclanche Battery. — One of the most convenient cells 
for open circuits, such as are used for door bells and in 
various alarms, is the Leclanche. It consists of a glass jar 
containing ammonium chloride (sal ammoniac) in which is 
placed a zinc rod and a porous jar. The porous jar contains 
a carbon plate very tightly packed with a mixture of man- 
ganese dioxide and graphite, or granulated carbon. This 
cell may be used continuously on such a circuit for a year 
without refilling, if it is kept tightly closed to prevent 
evaporation. In preparing this cell, about ten parts of 
water to one of sal ammoniac are needed. 



Fig. 96. 



EFFECTS OF ELECTRIC CURRENTS. 

Heating Effects. — Experiment 88. — Place a short piece of small 
platinum wire in the circuit of a strong battery and note the result. In 
the battery chemical action is transformed into heat and an electric 
current. If the current does no work, all of this chemical energy is 



128 Elements of Physics. 

transformed into heat in the circuit. The relative amount of heat in- 
side the cell and in the outside circuit are proportional to the internal 
and external resistance. Thus, if the platinum wire were not inserted 
in the outside circuit, the heat in the Uquid of the cell would be greater. 

The practical applications of this property of an electric 
current are very numerous : electric Hghting, cooking and 
heating, blasting, and exploding mines, torpedoes, and 
firearms, are examples. 

Chemical Effects. — Experiment 89. — Into a U-shaped glass tube 
about one half an inch in diameter and i o inches long, fit corks through 

which insulated copper wires extend 
having strips of plantinum soldered on 
the ends in the tube (Fig. 97). Sup- 
port the tube in a frame and fill it 
about two-thirds full of copper sulphate 
solution colored with blue litmus or in- 

dioQ. Connect the outer ends of the 
Fig. 97. ^ 

wires with a strong battery. Bubbles 

at once begin to rise from the plantinum strips, and in a few minutes 

the liquid around the positive pole turns red, showing the presence of 

acid, while the negative pole is covered with a coating of metallic 

copper. 

Repeat the same experiment, using a ten per cent solution of water and 

sulphuric acid, and note the result. The current decomposes these 

liquids, often separating compounds into their elements. 

Electrolysis. — The process resulting in Exp. 89 is 
called electrolysis, and the liquid decomposed is called an 
elect7vlyte. By a careful study of the bubbles that rise from 
the electrodes in the experiment with the water and sul- 
phuric acid it will be noticed that about two volumes of 




Electro-Dynamics. 



129 



gas will rise from the negative electrode to one from the 
positive. By collecting and examining these two gases, 
that coming from the negative electrode will be found to 
be hydrogen and that from the positive oxygen. This is 
an illustration of an electrolysis in which the elements 
forming a compound are separated from each other. 

Experiment 90. — Dissolve a few grains of potassium iodide in a 
little water and make a paste by boiling pulverized starch in water. Mix 
these thoroughly and spread the mixture over a blotter. Attach the 
negative electrode of a battery to the moist part of the blotter and draw 
the positive electrode over the paste. This electrode marks upon the 
blotter as if it were moistened with purple ink. This electrolysis de- 
composed the potassium iodide, and the iodine united with the starch 
to form a new compound. 



Magnetic Effects. Galvanometer. — If a wire through 
which a current of electricity is passing is held parallel 
and close to a magnetic needle, the needle will be de- 
flected. The direction and extent of the deflection will 
depend upon the direction and strength of the current, 
and upon whether it is above or below the needle. Try 
the experiment. A compass is thus used to detect the 
presence of electricity 
in a conductor; by 
placing the needle 
over a scale gradu- 
ated in degrees, any 
current may be compared with any other current, and 
hence measured. The effect is increased if a coil of in-, 
sulated wire be placed about the needle (Fig. 98). Such 
an arrangement constitutes a galvanometer. Upon this 
principle electrical measurements are based. 




Fig. 98. 



130 Elements of Physics. 

Direction of the Current. — The direction of the current 
through a conductor may be shown by the use of a com- 
pass as follows : place the conductor over the needle and 
parallel to it. If the needle points northwest or in a 
westerly direction, the current is going north ; if it points 
northeast or in an easterly direction, the current is going 
south. Place the conductor below the compass, and the 

deflections of the 

'^ ii^mmm^m mmim > needle will be oppo- 

P^^ site to the above di- 

rections. 

If a wire through which a strong current is passing is 
dipped into iron filings, they will cling to the wire and 
arrange themselves in circular lines around it (Fig. 99), 
giving a representation of the magnetic field set up by a 
current of electricity. 

If the same wire is passed vertically through a piece of 
cardboard and fine iron filings sifted on the card, the 
filings arrange themselves in 
whirls around the wire, and a 
small pocket compass placed 
anywhere in the field will 
always lie tangent to the lines 
of force (Fig. 100). If the 
current be reversed, the needle 
will be reversed, but will re- 
main tangent to the lines of 
r Fig. 100. 

force. 

If the conductor be bent in a circle, the lines of force 
will have vortical direction, as represented by Fig. lOi. 




Electro-Dynamics. 1 3 1 

If several turns be made in the conductor, the result 
will be as indicated in Fig. 102, and the lines of force will 
assume the same form and direction as in an ordinary bar 
magnet. 





Fig. ioi. Fig. 102. 

" Every conducting wire is surrounded by some sort of 
magnetic whirl. A great part of the energy of the electric 
current in the wire consists in these external magnetic 
whirls. To set them up requires an expenditure of energy, 
and to maintain them requires a constant expenditure of 
energy." (S. P. Thompson.) 
In fact, the current and lines I 

always co-exist, and one varies 1 

directly as the other, when 
no magnetic substance is in 
the field. It is the energy 
of these whirls which acts 
upon all substances brought 

within their range. They turn the magnetic needle, and 
cause it to stand at an angle to the conducting wire. The 
intensity of the magnetic field may be increased by increas- 
ing the number of turns of wire, because of their combined 
action. A coil like that shown in Fig. 103 is called a 



132 



Elements of Physics. 



solenoid, and the current in passing through it produces 
polarity in it the same as in a magnet. 

Experiment 91 . — Ar- 
range a solenoid, and 
suspend it with the lower 
end dipping in mercury 
(Fig. 104), so that it will 
take a current through it 
and be free to swing. 
Pass a strong current 
through the solenoid, and 
with a magnet test it for 
polarity. Now let the so- 
lenoid become still, and it 
will point north and south. 




Fig. 104. 



Hold a straight current-bearing wire parallel to it, and compare its 
action with that of the magnetic needle. 

Add another similar coil, so made that it can be handled easily 
(Fig. 105), and while passing a strong current through both of them, 
test for polarity and other 
magnetic properties. — '^ 

Effects of Parallel Cur- 
rents. — Experiment 92. 
— Take a square block and 
wind about a dozen turns 
of insulated wire upon it, so 
as to make a rectangular 
coil (Fig. 106), A^ and sus- 
pend it as above. Connect 
a battery to it, and determine the direction of the current. Make 
another similar coil, B^ connect it to a battery, and determine the direc- 



FiG. 105. 




Electro-Dynamics. 



133 



tion of its current. Now hold B so that its current will be parallel to 
the current in A^ and in the same direction. Note the result, then turn 
B so the currents 

^' ""^ ^ 

A B 



will go in opposite 
directions, and com- 
pare results. From 
these experiments we 
learn — 

Ampere's Law 
of Electric Cur- 
rents. — Parallel 
currents attract 

each other when in the same direction^ bnt repel eacJi other 
if in opposite directions ; currents 7iot parallel ha.ve a ten- 

dency to become parallel a7id to 
flow in tlie same direction. 




^>rTr^ 



Fig. 106. 



D^ 




Fig. 107. 



The cause of this attraction 
may be seen by a careful study 
of Fig. 107, in which A and 
B are two parallel conductors 
with their currents going in 
the same direction, with the 

magnetic whirls around them. It is easy to conceive 

that the lines of force instead of 

going in opposite directions at 

C would be more likely to take 

the same general direction, ED, 

and go around both conductors ; 

this would cause the lines to tend 

toward a circular path, and in doing so pull the conductors 

together. 




Fig. 108. 



134 Elements of Physics. 

The corresponding phenomena of repulsion may be 
understood by a study of Fig. io8, in which the currents 
run in opposite directions and the lines of force lie in 
opposite directions. In this case, the Hues are running 
together at C in such a way that there is a tendency to 
push the conductors apart. (Compare with the theory of 
attraction and repulsion in magnetism.) 

Current Induction. — By making use of the magnetic prop- 
erties of electric currents as just studied we are enabled to 
produce a wonderful influence over any magnetizable sub- 
stance. For instance, we know that any magnetizable 
substance brought within the field of a magnet absorbs 
many of the lines of force, distorts the iield, and becomes 
magnetized. Now, since the lines of force produced by 
an electric current are identical with those of a magnet, 
it is evident that a magnetizable substance in the field of 
an electric current will absorb the lines of force, distort 
the field, and become magnetic by induction. It is also 
evident that a magnetizable substance placed within 
a solenoid will absorb the lines of force and become a 

magnet. 

Experiment 93. — Wrap several turns 
of insulated wire around a small iron bolt 
or large spike (Fig. 109), then send a 
current of electricity through the wire, 
and test for magnetization. Break the 
Fig. 109 circuit, and the iron will lose its magne- 

tization. Increase the number of turns 
in the wire several times, and compare the strength of the magnetiza- 
tion with that in the first case. 




Electro-Dynamics. 



135 




Electro-magnets. — In this arrangement the bolt is 
called a core, the coil of wire a helix^ and both together 
an electro-magiiet. The core is 
sometimes bent into a U-shape, 
so that the magnetic force of 
both poles may be utilized. More 
frequently two iron rods are used 
(Fig. no) to facilitate the wind- 
ing, and are fastened together 
by a third piece, F, called the 
yoke, in order to make it all act 
as one rod. A piece of soft 

iron, A, called the m'matitre, is used on the poles for 
working purposes. 

Since the intensity of a solenoid's effect depends upon 
the number of its lines of force, and the number of its lines 
of force depends upon the number of turns in the conduc- 
tor, it is evident that the strength of an electro-magnet de- 
pends upon the number of turns of the conductor around 
the magnetizable substance. By using many turns in the 
helix and a very strong current, electro-magnets have been 
constructed which would lift thousands of pounds. 

Electro-magnetic Induction. — While it is true that any 
magnetizable substance brought within the field of an elec- 
tric current becomes magnetic, it is also true that when 
magnetic lines of force are disturbed by a conductor, they 
set up a current of electricity in that conductor. 



Experiment 94. — Take a helix of many turns so arranged that a 
bar magnet may be slipped freely in and out of it (Fig. in), and 
attach a galvanometer to it. Slowly lower a magnet into the coil and 



136 



Elements of Physics. 



note the effect upon the galvanometer. Now move the magnet in and 

out of the helix slowly, then 
rapidly, and it will be noticed 
that the galvanometer is affected 
only as the magnet moves, and 
that the faster the movement, the 
o;reater the effect. 




Fig. III. 



We have seen that all 
electric currents possess 
magnetic properties, and 
will deflect a galvanome- 
ter needle ; hence, when 
we move the needle by 
the method used above we must infer that a current 
of electricity is set up in the conductor. The direc- 
tion of the current through the conductor depends 
upon the direction of the motion producing it. Every 
magnetic change tends to produce an electric current in 
•whatever conductor happens to be near. This action is 
called electj'o-magnetic mdiiction, and it is of the utmost 
scientific importance, since nearly all of the practical ap- 
plications of electricity are based upon it. It must be 
borne in mind that the mere presence of a magnet or 
current near a conductor produces no effect whatever. 
They must be moved or changed in strength. 

The explanation of this phenomenon is this : The motion 
of the inducing lines of force generates whirls around the 
conductor; and as these whirls and an electric current 
always coexist, when one is generated the other is mani- 
fest. This might be illustrated by taking a very large helix 
made of wire around which are many small rings, and a 



Electro-Dynamics. M7 

flaring paint brush. By pushing the brush through the 
helix it will set the rings turning, and by pulling it out they 
will be made to turn in an opposite direction. To produce 
this motion of the rings requires energy, for there is 
work to be done. The bristles of the brush represent the 
lines of force of the magnet, and the rings represent the 
whirls of force produced. The faster the brush moves, 
the more rapid the motion of the rings, and vice versa ; 
hence the faster the magnet moves, the greater the effect, 
i.e. the greater the intensity of force whirling around the 
conductor. These facts show us why there must be some 
change either in position or intensity in the lines of force 
of the inducing body if electricity is to be generated by 
induction. There can be no motion unless there is antece- 
dent energy, the greater the energy, the greater the result ; 
and the greater the work to be done, the more energy 
necessary; the greater the resistance overcome, the greater 
the energy which becomes manifest. The work to be done 
by electricity is called resistance. 

Induction Coil. — When the above operations are kept up 
continuously and rapidly, great results may be obtained. The 
essential features of an instrument constructed upon this 
principle are shown in Fig. 112. The instrument is known 
as an inditction coil. When the current is turned on, it 
passes through the platinum point, A^ to the hammer, //, 
and through the primary coil, P, which is an electro-mag- 
net, and back to the battery. The current magnetizes P 
and this draws H away from A, thus breaking the circuit. 
As soon as the current is stopped, H iiies back against A, 
only to be drawn away again by the passage of the cur- 
rent. In this manner H is kept vibrating rapidly to and fro, 



138 



Elements of Physics. 




Fig. 112. 



alternately closing and opening the circuit. By this action 
a current is set up in the primary coil and an induced cur- 
rent in the secondary 
coil, vS, which lies in 
the field of the electro- 
magnet. The primary 
coil consists of a few 
turns of coarse wire, and 
the secondary of many 
turns of fine wire made 
so that it will slip over 
the primary but having 
no electrical connection 
with it. On account of the rapidity of the vibration of 
H some residual electricity is left in the primary, and 
to remove this, Ruhmkoff added a condenser, C, This 
consists of layers of tinfoil insulated from each other and 
connected alternately with the positive and negative elec- 
trodes of the battery. 

Electrical Units. — Resistance is that which obstructs the 
flow of electricity through a conductor. The unit of resist- 
ance is the ohm. It is equivalent to the resistance of a 
column of mercury i square millimeter in cross-section 
and 1.06 meters long or of 9.3 feet of No. 30 copper wire. 
Ordinary telegraph wire offers a resistance of about one ohm 
to every 300 feet, or about 1 7 ohms to the mile. There is 
resistance in all parts of a circuit. That in the fluid of the 
cell is called internal resistance, and that in the outer cir- 
cuit external resistance. All resistance within the generator 
is waste energy, but that without is not waste energy because 
it is transformed into heat, light, and magnetic or mechani- 
cal energy. 



Electro-Dynamics. 139 

Laws of Resistance. — I. The resistance of a conductor is 
proportional to its length. For example, a wire of the same 
diameter and material will have twice as much resistance 
for two miles as it will for one. 

II. The resistance of a conductor is inversely proportional 
to the area of its cross-section ; in the case of a round con- 
ductor to the square of its diameter. Thus, if No. 24 wire 
has a diameter twice that of No. 30 wire, the same length 
of the No. 24 will show four times the resistance of the 
No. 30. 

The resistance of any conductor may be measured, 
whether it be the circuit of an ordinary laboratory battery, a 
telegraph line, or an ocean cable. 

The simplest method of measuring resistance is that 
known as substitution. The conductor to be measured is 
placed in a circuit with an ammeter (a galvanometer gradu- 
ated in amperes) and the current strength noted, then it is 
replaced by a resistance box and as many coils added as are 
needed to produce the same result as before. Another 
method of measuring resistance is by the use of Wheat- 
stone's bridge (Fig. 113). W 
is the wire the resistance of 
which is to be measured, and 
R the resistance box whose 
values are known. Plugs are 
removed from the resistance 
box until the galvanometer, G^ 
shows no current, then the 
sum of the coils in the resist- 
ance box that have been put in the circuit will be the 
resistance of W, The principle upon which this measure- 




140 Elements of Physics. 

ment is based is that when the potentials of E and F are 
equal no current will flow through the galvanometer, G. 

Electro-motive Force. (E.M.F.). — The electromotive 
force is that which causes the electricity to flow in a circuit, 
and is termed voltage or electric pressure. It represents 
the difference of potential between two points. In the 
battery it is the difference of potential between the two 
electrodes. The practical unit of E.M.F. is the volt^ which 
is a little less than the electric pressure of one Daniell cell. 
The following are the voltages of some important cells : 
Daniell, i.i volts; Bunsen, 1.8 volts; and Grenet, 2 volts. 
For measuring voltage a voltmeter is used. The pressure 
of any cell can be measured by connecting it carefully with 
the instrument. Care must be taken that all metallic con- 
nections are good. Verify the voltages of the cells above 
mentioned. 

Current Strength. — The unit of current strength is the 
ampere. It is the current produced by an E.M.F. of one 
volt working against a resistance of one ohm. 

Ohm's Law. — The relation of the three units — volt, 
ohm, and ampere — is suggested in the definition of the 
ampere. From what has preceded we learn that the 
E.M.F. tends to urge a current forward, while resistance 
tends to check it; the resulting current therefore shows 
how much greater the E.M.F. is than the resistance. This 
relation was formulated in the following law by Dr. Ohm in 
1827 : The cicrrent from any given source varies directly as 
the E.M.F.y and inversely as tJie resistance^ or C=^ E -^ Ry 
in which C= current, E = E.M.F., and R = resistance. In 
a battery the internal resistance is designated by r, and the 
formula becomes C= E ^{R +r). 



Electro-Dynamics. 



141 



Application of Ohm's Law. — An examination of the for- 
mula, C = E -^{R + r) will reveal the fact that C may be 
increased either by increasing E or by diminishing R + r. 
In battery currents this may be effected by methods of cell 
connection. The positive pole of one cell may be con- 
nected with the negative of the next, and so on, causing the 
current to pass through each individual cell. The poten- 
tial of the first cell is added to 
that of the second, and the sum 
of these to the third, etc., mak- 
ing the E.M.F. of the battery 
equal to the sum of all these 
potentials. This connection 
is known as series (Fig. 114). 
The E.M.F. is found by multi- 
plying the number of cells by 
the E.M.F. of one cell. This 
arrangement is economical when 
the external resistance is large 
and requires a high E.M.F. to overcome it. The best 
results are obtained when the external and internal resist- 
ances are nearly equal. 

If the external resistance is small, little can be gained 
by increasing the E.M.F., and for such conditions a form of 

connection known as 
parallel or multiple 
arc is adopted. By 
this method all the 
positive plates on 
one side and all the 
negative plates on the other are connected, making a 
large battery whose plate area equals the sum of all the 




Fig. 114. 



wmt 




Fig. 115. 



142 Elements of Physics. 

plates but whose E.M.F. remains the same as that of a 
single cell. The only advantage derived is diminished 
internal resistance by increased cross-sectional area of the 
liquid conductor (Fig. 115). If the number of plates be 
represented by n^ the internal resistance will be i divided 
by n times that of a single cell. 

The relative advantages of the series and parallel con- 
nections may be shown as follows : A battery of 8 cells, 
each having a voltage of 2 and an internal resistance of .5 
ohms acts, first, through an external resistance of .2 ohm, 
and secondly, through an external resistance of 200 ohms. 
Which method of grouping would produce the better 
result } 

By joining the cells in parallel, when i? = .2 ohm, (7=2-5- 
f .2 + *-^ ] =8.57 amperes, and when R = 200 ohms, C= 2 -^ 

200 -f- — = .0099 ampere. 
8 

By joining them in series, when 7? = .2 ohm, C= 8 x 2 
-^(.2 -h 8 X .5) = 3.8 amperes and when R = 200 ohms, C 
= 8 X 2 -f- (200 -h 8 X .5)= .078 ampere. 

COMMERCIAL APPLICATIONS OF ELECTRICITY. 

Electrotyping. — Electrotyping is the making of a cast of 
an object by the gradual deposition of a metal from a solu- 
tion by means of an electric current. If two pieces of clean 
platinum are put into a solution of copper sulphate, no 
change occurs ; but if an electric current is sent through 
the cell, copper at once begins to coat the negative plate. 
If the current is reversed, the copper will be transferred to 



Electro-Dynamics. 143 

the other plate, ahvays being deposited on the negative, 
Le, the one where the current leaves the solution. By 
continuing the current and strength of the solution, the 
deposit may be made of any thickness, and by varying the 
current, solution, and temperature, its texture may be made 
hard and brittle, or tough and malleable. 

If it is desired to obtain an electrotype for printing a 
book, a page is set in type, then an impression of this made 
in a wax surface. This wax surface is then made a con- 
ductor by thoroughly brushing it with black lead. It is 
then suspended in a bath of copper sulphate dissolved in 
dilute sulphuric acid and attached to the negative pole of a 
battery or dynamo. A copper plate is suspended from the 
positive plate just above the wax. The copper sulphate is 
decomposed by the current, and copper is deposited on the 
mold. When it is about one one-hundreth of an inch 
thick, it is removed and backed by type metal to give it 
firmness ; then it is fastened to a block of wood to make 
it type high. It now shows every line in the types or 
engraving and is ready for the printer. 

Electroplating. — Electroplating is the process of cover- 
ing articles made of cheaper metal with gold, silver, plati- 
num, or other costly metals by means of an electric current. 
Articles to be plated are carefully cleaned and then dipped 
into a solution of nitrate of mercury, from which they get a 
coating of mercury which causes the plate to adhere firmly. 
They are then suspended from the negative pole, with a 
plate of the metal desired in the plating suspended oppo- 
site them from the positive pole, and entirely covered by 
the electrolyte. The bath for gold, silver, or platinum con- 
tains 100 parts water, 10 parts potassium cyanide, and i 



144 



Elements of Physics. 



part of a cyaaide of the metal to be used. Many articles 
are plated with copper before putting on the finer metal, 
in order that the plate may stay on better. This process 
is very important in the arts and involves but little expense. 

Electric Bells. — One of the simplest uses of the electro- 
magnet is in the ringing of door bells, telephones, alarms, etc. 

Fig. ii6 represents the essen- 
tial parts. E is the electro- 
magnet, A the armature fas- 
tened by a spring, 5", which 
holds it away from the poles of 
E. When the current passes 
through the magnet, it draws 
A toward it so that the ham- 
mer, H, strikes the bell, B, and 
at the same time breaks the 
circuit by separating A and the 
screw, P, As soon as the cir- 
cuit is broken, E is demagne- 
tized, and wS springs back and strikes P, again closing the 
circuit and causing the above action to be repeated. The 
making and breaking the circuit is done in rapid succession 
and causes the bell to ring as long as the circuit from the 
battery is closed : this is done by pushing the button, D. 

Electric Telegraph. — The electric telegraph has for many 
years been the principal means of rapid communication 
between widely separated points. It consists essentially of 
two electro-magnets with vibrating armatures and a cur- 
rent breaker, K^ called a key, at each end of the line 
(Fig. 117). One of the magnets, 5, is called the sounder, 
and the other, i?, is called the relay. These instruments 




Fig. 116. 



Electro-Dynamics. 



H5 



are so arranged that an electric current may be sent a long 
distance and produce signals by which information of any 
kind may be given or received. The sending operator 
controls the current by the key. This consists of a plati- 
num contact point so mounted on a lever that it will close 
the circuit when the knob is pushed down. By pushing 
the key down, the sending operator causes the current to 
flow over the line and through the sounder at the other 
end, and the motion of its armature will exactly coincide 
with that of the key. When the circuit is closed by the 



station 



Line 



Station 




Fig. 117. 



key, the armature of the sounder is pulled down with a 
click ; and when the key is raised, the current is stopped 
and the armature springs up, causing a different click. 

When the line is very long or a great many instru- 
ments are to be operated at once, the current may not be 
strong enough to work the sounder directly, so a repeater or 
relay is used. It consists of a large electro-magnet made 
of small wire and carrying a pivoted armature similar 
to that of the sounder. The small wire multiplies the 
effect of the current. The armature has a plantinum 
point so attached that when it is drawn down by the magnet 



146 



Elements of Physics. 



it closes the local circuit and causes the sounder to click 
simultaneously with it. 

The code of signals used is composed of different com- 
binations of dots, dashes, and spaces ; that is, of short and 
long impulses of the current over the wire, as follows : 

A — B C... D E. F G H 

I.. J K L M N — 0. . 

P Q R. .. S... T— U V 

W X Y.. .. Z... . &. ... 

Telegraphing without Line Wires. — We have learned 
that a magnetic field extends in all directions radially from 
the magnet, and that it is limitless, though its force de- 
creases as the square of the distance increases. This is 
also true of the electro-magnetic field. The primary of an 
induction coil induces in the secondary a current which is 



B 






"^^fiiir^l^^ 




Fig. 118. 



capable of very high electrical pressure or potential. Now 
since the magnetic field of the primary is limitless, it is 
reasonable to infer that it will affect the secondary at what- 
ever distance they may be separated. The reason that we 



Electro-Dynamics. 147 

do not detect the influence is because it is too delicate for 
ordinary current detectors. Fig. 118 represents a very- 
successful method by which messages have been sent from 
sixty to one hundred miles and more. A is the sending 
station at which C is the primary coil, D the current 
breaker and C the secondary of a very powerful induction 
coil, with fF as a leading-out wire over which the pulsations 
are sent. B is the receiving station, at which A^is a very 
delicate microphone, called a coherer, especially constructed 
of iron or nickel filings. E is an electro-magnet or relay 
which closes the local circuit, and W^ is the receiving wire. 
When the instrument at A is operating, the immense 
magneto-electric whirls around W set up corresponding 
whirls around W^ y and the message becomes intelligible at B. 

Multiple Telegraphy. — There are various arrangements 
of the Morse telegraph now in use by which a single wire 
may be made to convey several messages at the same 
time, some in one direction and some in the other, without 
conflict. For full description of multiple telegraphy see 
Johnson's Universal Cyclopaedia, or Sharpless 8: Philip's 
Natural Philosophy. 

The Telephone. — - In our study of sound we learn that 
the vibrations of the membrane of the string telephone (see 
Sound) are the same as those of the body causing them, 
and that they are delivered to the other end of the line 
exactly as received. If a membrane of iron were used, 
it would perform the same vibratory motion, though 
not so appreciably on account of its mass and density. 
Now if the iron be brought near the pole of a magnet 
about which is a coin of insulated wire, the action 
between the magnet and the iron causes a current of 



148 Elements of Physics. 

electricity to traverse the wire, either this way or that, 
as the iron vibrates toward or away from the magnet. If 
connecting wires lead out to a similar distant instrument, 
the fluctuating current will cause the plate to vibrate in the 
same way by the magnet's varying attraction for it. If 
the first is vibrated by speech, the second reproduces it. 
This is a magneto-telephone, and constitutes what was origi- 
nally known as the Bell telephone. The instrument just 
described has been universally used as a receiver, but has 
been superseded by a more powerful apparatus, the micro- 
phone, as a transmitter. 

The Blake transmitter is the best known, and is shown in 
Fig. 119 in connection with the line and receiver. D 
is a sheet iron diaphragm against which lies a platinum but- 
ton, K^ suspended by a spring. A, and resting lightly against 
a carbon button, C, suspended by the spring, wS. K and C 
are the electrodes through which a current passes from the 
battery, B, The connection between K and C is in reality 



Fig. 119. 1 1 

always made, but the resistance of the electrodes changes 
by impress upon them when in light connection, and varies 
directly as the degree of impress. This being true, the 
current passing through the electro-magnet of the receiver 
varies accordingly. Hence, when the voice or some other 
vibrations produces an impress upon the connections, these 
vibrations are transmitted to the receiver, Ry and its vibrat- 



Electro-Dynamics. 



149 



ing armature, AB, vibrates simultaneously and reproduces 
the impressed vibrations. When it is desired to give trans- 
mission over long lines, the direct microphone current is 
sent through the primary of an induction coil, My in whose 
secondary the receiver is placed. By this arrangement 
music has been transmitted over 2000 miles. 



f 


1 


V 



/¥" 



Fig. 120. 



V! 



^ 



> 



The Electric Motor. — From our knowledge of magnets 
we can see by a study of Fig. 120 that 
either magnet has a tendency to move the 
other and to be moved by the other, and 
that if the magnets were free to move, 
they would become parallel. It is further 
evident that if a scheme can be devised 
for maintaining such a relation as repre- 
sented, and one of the magnets be free to 
move, continuous rotation of that magnet will be the result. 

By the use of electro-magnets (Fig. 121) such a scheme 

is maintained, and the electric 
motor is the result. Ay B^ C, 
and D represent the spokes of 
a solid iron wheel insulated 
#from its axle. D and C are 
wound by a coil of insulated 
wire, making an electro-mag- 
net. A and B are also wound, 
hence ABCD is an electro- 
magnet with its poles at A and 

B ox ?iX,C and D, depending upon which pair of spokes the 

current is going around. 

By a device, (9, formed of four strips of copper, i, 2, 3, 
and 4, called the commutator, and two copper brushes, X 




Fig. 121. 



I50 



Elements of Physics. 



and F, the current is made to pass round AB or CD only 
when at a large angle with a line from Nto S. While in 
the present position, CD is the magnet, and the mutual 
attraction and repulsion between it and the field magnet, 
NSy turn the wheel as indicated by the arrows. But when 
it has gone one fourth round (or a little less), AB becomes 
the magnet, and taking the place of CD turns as CD did. 
In this manner the action is continuous as long as a current 
flows through. 

Electric motors may have any number of parts like AB 
and CD ; usually an even number is employed. By strong 
currents and well-calculated levers and wheels, very heavy 
loads, as electric cars, fans, lathes, and machinery of all 
kinds, may be moved by such a motor. 



The Dynamo. — While the motor is a machine for con- 
verting electrical energy into motion, the dynamo is a 

machine for converting mechani- 
cal motion into electrical energy. 
It is based upon the principle of 
current induction and contains a 
series of closed coils, called the 
armature, revolving in a magnetic 
field in such a way that the number 
of Hues of force cut, and the di- 
rection in which they are cut varies 
continuously. The manner in which 
these changes are made is shown 
in Fig. 122, in which TV^and vS are the poles of the field 
magnet and CDEF a single coil that may be rotated 
between them. In its present position the greatest pos- 




FlG. 122. 



Electro-Dynamics. 151 

sible number of lines of force will pass through it. As it 
rotates, this number decreases until it has turned one fourth 
of a revolution, at which point the number becomes zero. 
During the next one fourth revolution the number of lines 
increases, and after the first half turn the direction in 
which the coil cuts them changes. 

This motion in the magnetic field sets up a current in 
the coil. Suppose its direction is as indicated during the 
first half turn, then it would be opposite during the next 
half, and so on. Every change in the direction of the cur- 
rent is called an alternation. Thus, if a machine produces 
300 alternations per second, it reverses its current 300 times 
per second ; t,e. it sends 150 currents in one direction and 
150 in the opposite direction each second, or there would 
be 150 complete to and fro currents per second. This 
number is called ciii'vent frequency, A metallic or carbon 
brush, m, touches the copper ring, h, and carries the cur- 
rent from one end of the coil, while another brush, //, car- 
ries it away from the other end and through the external 
resistance, R. Such a machine is called an alte7'7tating 
current dynamo. 

The Commutator. — In order to have the oppositely di- 
rected currents of the dynamo flow in the same direction 
through the external circuit a special device called the 
commutator is used. For the dynamo just described it 
would consist of a brass tube divided into two parts by 
cutting it lengthwise (Fig. 123). These two segments are 
insulated from the axis of the armature and connected 
with the separate ends of the coil. The brushes bear 
on the commutator and are so arranged that they ex- 
change connections with the cummutator strips at the 




152 Elements of Physics. 

same time the current reverses in the coil. In this way 
one is always kept positive and the other negative, making 
the current direct through the exter- 
nal circuit. In a dynamo armature 
having more than one coil there are 
two diametrically opposite commuta- 
tor strips to every coil, and the num- 
ber of alternations per second varies 

as the number of coils and rotations 
Fig. 123. 

of the armature. The dynamo is 
a very efficient machine, reproducing nearly 95 per cent 
of the energy that is turned into it. 

Electric Lighting. — When the passage of an electric cur- 
rent is greatly hindered, heat is produced, and when it is 
broken, a spark may be seen at the place of rupture. If the 
pressure is very great, as 45 or 50 volts, the current is not 
always broken when the metallic circuit is broken ; i,e, after 
the current is started the ends of the conductor may be sepa- 
rated a very short distance, depending upon the voltage and 
kind of material of the broken conductor. It is customary 
to use sticks of carbon so fixed that part of the current 
operating an electro-magnetic device keeps them about 
one tenth or one eighth of an inch apart. When the ends 
are separated, the current heats them to a white heat, which 
makes a very brilliant light. The hght is caused by the 
incandescence of particles of carbon which in the form of 
luminous vapor fly from the positive terminal to the nega- 
tive, making it cone-shaped and leaving the positive crater- 
shaped. The formation of the luminous vapor gradually 
destroys the carbon. All of the lights in a circuit require 
the same number of volts, and as they are connected in 



Electro-Dynamics. 



153 



series (Fig. 124), the voltage of the circuit depends upon 
the number of lamps to be lighted. For instance, 100 
lamps of 45 volts each, require a current of 4500 volts. 




-#- 



Arc Lights Direct current 



-@- 



FiG. 124. 



The current strength for each arc is generally from 8 
to 10 amperes. A circuit of 100 lamps of 45 volts each 
represents the energy of about 60 horse power. 

Incandescent Lighting. — This name is given to the light 
because a part of the conductor is made of a substance of 
very high resistance which the current raises to a white 
heat. This part of the conductor is usually a carbon fila- 
ment inclosed in a glass bulb from which the air has been 
exhausted to keep the intense heat from decomposing the 
carbon by union with oxygen. The light is due directly to 
the temperature, and most lamps have filaments such that 



Transformer 



Incandesce) 
Q 6 A 4 A 



nt Liglits 




Alternating current 
from dynamo 



Fig. 125. 

a current of .5 to .6 ampere gives from two to three candle 
power per inch. Incandescent lights are arranged in par- 
allel ; that is, two main conductors lead out from the dynamo 
and transformer and the lamps are connected at intervals 
between them, as in Fig. 125. Any lamp thus connected 



154 



Elements of Physics. 



will have a current through it depending upon the resist- 
ance of the lamp. Thus, if the voltage is 50 and the lamp 
resistance 100 ohms, the current will be .5 of an ampere. 

The Transformer. — In Fig. 125, O is an induction coil 
used in incandescent lighting to change the relation of the 
number of volts to the number of amperes in any current. 
In a perfect transformer the number of volts in the primary 
multipHed by its amperes equals the number of volts in the 
secondary multiplied by its amperes. For instance, if the 
voltage in the primary is 1000 and the current i ampere, 
the energy equals 1000 times i or 1000 watts (electrical 
energy unito). The transformer hands over this energy 
from the primary to the secondary. It does not increase 
the energy, though it may by some losses diminish it. If 
the voltage in the secondary is reduced, as to 100 volts, the 
number of units of energy must still be 1000, hence the 
number of amperes would be 10. 

The Ruhmkorff coil (Fig. 126) as described changes 
a current of low potential to one of high potential, and 

is called a ^/<f/- 
/// transformer. If 
a coil of fine wire 
be used as the pri- 
mary, the current is 
changed from one 
of high potential to 
one of low poten- 
tial, and the appa- 
ratus is called a 
step-dozvn transformer. In lighting private houses step- 
down transformers are used to bring down the high poten- 




Electro-Dynamics. 155 

tial of the main circuit to the safe Hmit of about 100 volts. 
By the use of transformers many hundreds or even thou- 
sands of amperes may be obtained for metal fusing and 
the like. 

Questions for Review. — i . What is static electricity ? 

2. What is electrical potential? 

3. What is positive electricity? 

4. What is the law of attraction and repulsion? How is it proved ? 

5. Describe the electroscope. How does it act? 

6. Explain the action of the electrophorus. 

7. What effect have points on electrical charges? 

8. Where does the Leyden jar get the charge that is on the outside ? 

9. Why will frictional electric machines not work well in damp 
weather? 

10. Why put a metallic shell around a powder house? 

1 1 . What is lightning ? How may we protect bodies from its effects ? 

12. What is the duration of a flash of lightning? Prove your an- 
swer. 

13. Why is it safe to be in bed during a thunder storm? 

14. Why is the air pure after a thunder storm? 

15. What is a voltaic cell? 

16. What are two of the best cells ? Describe them. 

17. What is amalgamation ? Its uses? 

18. Explain the different cell connections and tell the advantage of 
each. 

19. What is meant by resistance? How is it measured? 



156 Elements of Physics. 

20. What is a galvanometer? Explain its action. 

21. What is induction? Its uses? 

22. Explain the work of induction in the telegraph ; in the tele- 
phone ; in the dynamo, transformer, and motor. 

23. What is the principle on which the motor acts? 

24. Why are arc lights in series ? 

25. Why are incandescent lights in parallel? 

26. What is a commutator? Is it used on all dynamos? Why? 

27. Explain electroplating. Electrotyping. 

28. What are electro-magnetic whirls ? How do we know they exist ? 

29. What is an ammeter? A voltmeter? 

30. Explain the action of the microphone. 



CHAPTER IX. 

SOUND. 

Acoustics. — That part of Physics which treats of the 
origin, transmission, and comparison of various sounds 
is called acoustics. 

Sound. — Sound is a peculiar manifestation of the energy 
of mass vibration. A vibrating body is one whose parts 
so move that each returns periodically to its starting point. 
The movement it performs between two successive passages 
in the same direction through any point is called a vibra- 
tion. 

Kinds of Vibration. — Vibrations are of three kinds, 
named from the direction of their movements. When the 
tongue of a jew's-harp is struck, it vibrates at right angles 
to its length. Such vibrations are called transverse vibra- 
tions. By taking a pendulum made of a long wire and a 
heavy weight, turning the weight around several times 
and then releasing it, we find that it untwists the wire but 
does not stop vibrating for some time. This is called tor- 
sional vibration. When a weight is suspended by a coiled 
spring and made to move up and down, it vibrates in a line 
with the length of the spring. Such movements are called 
longitudinal vibrations. 

In each of the above illustrations the entire distance 
through which the body moves in making a vibration is 
called its ainplitnde, and the time taken to make such 
movement is \\\^ period of vibration, 

157 



158 Elements of Physics. 



Sources of Sound. — Experiment 95. — Strike a tuning fork. 
Note the sound. Strike it again and hold the outer end in water. The 
water is disturbed and splashes. This shows that the fork is vibrating. 

Experiment 96. — Fasten a small copper wire to one prong of a 
tuning fork. After striking the fork draw it over the surface of a smoked 
glass so that the tip of the wire will lightly drag through the lampblack. 

Hold a tumbler or air- 
pump receiver horizontally, and lay a penny inside near the rim. 
Strike the tumbler. Note that sound is produced and that the penny 
dances up and down, causing a rattle. 

If we tie a bullet to a string and let the bullet swing against the side 
of a sounding bell, a similar result will be noticed. 

Experiment 98. — Support an electric bell on pieces of felt under 
the bell jar of an air pump. Start the bell and begin to pump the air out 
of the jar. As the air is pumped out, the sound of the bell grows fainter 
and fainter until it finally becomes inaudible, though the motion of the 
hammer is plainly visible. 

In the above illustrations we notice that the energy of 
mass vibration is manifest. In our attempts to trace this 
energy we discover that there must be an intervening 
medium through which it can travel. 

Transmission of Sound. — Knowing that the tuning fork, 
bell, etc., must be elastic in order to vibrate, we infer that a 
medium must be elastic that it may carry or transmit these 
vibrations. The question now arises, how is sound trans- 
mitted through this medium ? 



Sound. 



159 




Fig. 128. 



Experiment 99. — Take a tube (Fig. 128) three or four feet long 
and cover one end, A^ with an elastic membrane. By burning a small 
rag fill the tube with 
smoke. Cover the 
open end with a fun- 
nel. Set a lighted 
candle so that the 
flame will be near the small end and directly in front of it. Now tap 
the membrane lightly with the finger, note the effect and compare the 
time of the stroke on the membrane with the effect upon the flame. 
Does the smoke come out when the membrane is tapped? Remove 
the membrane and strike two books together before the large end of 
the tube so as to make a noise, and note the result as before. 

This experiment shows that the air in the tube does not 
move forward in a body, but that the vibrations of the mem- 
brane, etc., are taken up by it and transmitted through it 
to the flame ; i.e. the flame is affected by a vibration of 
air, and not by a current. 

For a more careful study of the transmission of vibra- 
tions through air note the following : — 

Experiment 100. — Suspend a row of pendulums of equal length 
from a bar or rod of wood (Fig. 129). Use marbles as bobs. Draw 

back pendulum bob A and 
let it swing through an arc 
of several inches, striking 
bob B. With little change in 
position of the intervening 
marbles C will fly off as indi- 
cated in the figure. The force 
of A has been transmitted to C by the elasticity of the intervening 
marbles. 




V 



Fig. 129. 






i6o Elements of Physics. 

The above experiments indicate that air is a medium 
through which sound is transmitted and suggests the man- 
ner in which it travels ; i.e. by a series of condensations and 
rarefactions following each other in simple wave motion 
to and fro along a straight line. Do other forms of matter 
transmit sound ? 

Experiment ioi . — Take two tin cans open at both ends and stretch 
a piece of rawhide over one end of each. Attach a string or wire to the 
middle of each piece of raw hide, and keeping the string or wire tight, 
hold the open end of one can to your ear, while a second person holds a 
watch at the open end of the other. The ticking of the watch is plainly 
heard ; but more plainly over a wire than over a string. 

Experiment 102. — Place your ear at one end of a long stick and have 
some one strike a tuning fork and place it against the other end of the 
stick. The sound is very distinctly heard. 

In each of the above experiments we note that sounds 
which cannot be heard through the air are transmitted by 
solids. 

Experiment 103. — Let two persons take positions several hundred 
yards apart along a barbed wire fence or a railroad. When one strikes 
the wire or rail a smart blow with a hammer, the other notices that the 
sound reaches his ear through the metal and not through the air. 

Experiment 104. — Take a short tube of large diameter, put one 
end to the ear and the other in water. Let another person take two 
stones and tap them together under the water several hundred yards 
distant. Note the result. 

The above experiments show that soHds and liquids as 
well as gases transmit sound, but the question arises, in 
what respects do their actions differ, and why ? 



lliJil 



Sound. i6i 

Experiment 105. — Stand about 200 yards from a railroad and have a 
second person stand on the road and strike a rail several blows with an 
ax. Notice that the sound is heard when the ax is in the air. By 
carefully measuring the distance and counting the seconds from the 
time the ax strikes until the sound is heard, the velocity of sound in 
the air may be determined. 

By standing on the railroad some distance from the person with the 
ax, and repeating the experiment, it will be found that the report is 
heard much more quickly through the rail than through the air, showing 
that sound travels faster through steel than through air. 

The Velocity of Sound. — By repeating experiments simi- 
lar to these, the velocity of sound in air has been found to 
be 1090 feet per second at a temperature of 32° F. ; this 
velocity increases about one foot per second for every 
rise of one degree in temperature. The velocity of sound 
in air is much less than that of Hght, and is also less than 
the velocity of a bullet ; hence, a rifle ball strikes before 
the report is heard, but the flash is seen before the bullet 
strikes. Wary game and water fowl often take advan- , 
tage of this fact and learn to dodge at the flash and so 
escape. 

The velocity of sound in steel is found to be about 16 
times as great as it is in air; in water it is about 4714 feet 
per second at 27° F. The latter fact was established on 
Lake Geneva, Switzerland, in 1827, as follows : Two boats 
were moored 14,000 yards apart. Under the water at one 
boat a bell was rung by means of a lever which ignited 
some powder at the same instant. At the other boat an 
observer noted the time between the flash of the powder 
and the sound of the bell. 



1 62 Elements of Physics. 

The velocity of all sounds made simultaneously and in the 
same medium is the same, whether high or low. If this 
were not true, music of a piano or band could not be appre- 
ciated at any distance from the instruments. 

The above experiments and facts show that different 
kinds of matter differ in respect to the rate at which they 
transmit sound waves. It has been proved by experiment 
that the velocity of sound throtigh any medium varies directly 
as the square root of the elasticity of the medinmy and in- 
versely as the square root of its density. 

Waves. — We have learned that sound is transmitted 
through air by a series of condensations and rarefactions fol- 
lowing each other in succession. When any form of energy 
is transmitted through a medium, it is believed to be carried 
by wave motion. 

Experiment io6. — Take a soft cotton rope about 14 feet long and 

stretch it along the table or floor by nailing one end fast and holding 

the other in the hand. 
B D 

v^/'^Ns^^^^^''^ C/'"^s,^^^'*"N. Raise the hand, then 



Pj^^ j^^^ quickly lower it, and 

notice the crestlike form 
which traverses the entire length of the rope. Tie several black strings 
around the rope and repeat. Watch one of these points, and note that 
it has simply a vibrating motion at right angles to the length of the 
rope, as A^B, C^D (Fig. 130). 

A further study of wave motion can be made by dropping 
a stone in still water and noticing that there is only an up 
and down motion of the water particles, with no perceptible 
forward motion. Simple harmonic motion is transmitted 
through other elastic media by a similar motion. 



Sound. 163 

The crest of a wave is its highest point (5, Fig. 130), 
while its lowest point is called a trough (C, Fig. 130), and 
the distance from one particle of a medium to another in 
the same phase is a wave lengthy i,e, from crest to crest, 
or from trough to trough. 

Children everywhere are given to bursting paper bags by 
blowing them full of air and striking them suddenly. Each 
bag produces a single loud report. The air being blown 
into the bag is somewhat condensed, but by the stroke it 
is very much more condensed before the bag bursts. This 
being true, the confined air suddenly and forcibly expands 
when the bag bursts, and in doing so condenses the outer 
air for a certain distance in every direction because of 
inertia of the latter. But owing to the inertia of the con- 
fined air, it leaves a rarefaction where before there was a 
condensation. If many bags were burst at the point in 
regular and rapid succession, there would be produced 
alternating shells of condensation and rarefaction, all hav- 
ing a common center and enlarging as they advance, their 
motion being similar to that of the water above mentioned 
except that the shells are spherical, not circular. In this 
case a condensation represents a wave crest, while a rare- 
faction represents a trough, and from condensation to 
condensation is a wave length. 

Interference. — If two sound waves of the same length 
proceed in the same direction or in opposite directions so 
that they coincide in their phases, they will strengthen 
each other ; but if they differ in their phases by a half a 
wave length, they will neutralize each other, and silence 
will result. This phenomenon is called interference of 
sound. 



164 



Elements of Physics. 




Experiment 107. — Take two T-shaped tubes, B and K^ and join them 
as in Fig. 131, using rubber tubes, /^and C, and attach a funnel, A^ to one 

end and a short 
tube, //, to the 
other. Hold H 
to your ear while 
some one else 
_ blows a whistle 

F^^- ^31. "' ^tA. If C and 

/^ are of such lengths that a rarefaction meets a condensation at B, 
silence will result ; but if either J^ or C be closed, the full, smooth tone 
will be heard. 

In this experiment we note that air confined in a tube 
carries sound better and farther than air in the open. This 
is because all the energy of the vibration is thrown in one 
direction. All speaking tubes illustrate this. 

Experiment 108. — Strike a tuning fork, and holding it over an open 
bottle, turn the fork slowly. At times no sound is heard, while at 
other times the sound is very distinct. When the fork is struck, con- 
densations and rarefactions are produced as the fork is rotated. Op- 
posite phases meet and produce momentary silence. This becomes 
clearer if we repeat the experiment with a good resonator tube. 



Beats. — If two notes are different and not in the same 
phase, they will produce a wavy or throbbing sound be- 
cause they alternately weaken and strengthen each other. 
These alternations in loudness are called deals. 

Experiment 109. — Strike the lowest white key of a piano or organ 
and the black key next above it simultaneously. Let the continuous 
waveline (AB, Fig. 132) represent the waves caused by the white key 



Sound. 



165 



and the dotted line the waves caused by the black key. As both are 
struck at the same time, their waves start together at A, but as the lower 
tone waves are less frequent, they must be correspondingly longer. At 
certain intervals, as at B. condensations will correspond with rarefac- 
tions and produce momentary silence — too short for the ear to catch, 




Fig. 132. 

hence the wavy, throbbing sound. The real sound as perceived by the 
ear might be represented by the line XYZ in the same figure. 

A tone produced as above is a pleasing tremulo, as are many others 
similarly produced by very low notes ; but when the higher notes are 
struck, the beats are so extremely close together that disagreeable and 
grating discords are produced. 



Resonance. — A peculiar property of a vibrating body is 
its power of setting other bodies to vibrating. If a wire 
be stretched in the air and set to vibrating, its note will be 
scarcely audible, because from its very small surface a very 
small portion of air can be set in motion. The same is 
true of a tuning fork, but if its stem be pressed upon a 
table or a box inclosing a mass of air, its note becomes far 
louder. This reenforcement of sound caused by attaching 
the sounding body to some other body is called resonance. 
The terms sounding board and resonator have different 
meanings, as will be seen by the following : -^ 



i66 



Elements of Physics. 



Experiment i io. — Hold one end of a large glass tube (A, Fig. 133) 
in water as represented. Strike an " A " tuning fork and hold it over 
the tube while gradually lowering or raising the 
tube in the water. At a certain point the tone of 
the fork is greatly increased, or reenforced. If a 
'' B " fork is used, it will be necessary to change 
the position of the tube if the sound of the tuning 
fork is to be reenforced. 




Fig. 133. 



From this we learn that a tube of a 
given length will reenforce one tone only. 
Such a tube is called a resonator. From 
our knowledge of pianos and other musi- 
cal instruments we know that a sounding 
board reenforces any note of the in- 
strument. Hence we see that any note 

whatever may cause a sounding board to vibrate. Such 

vibrations are called forced vibrations. 

Experiment hi. — Sing several clear notes into a guitar, violin, or 
piano. By careful trial you will strike a note to which some string on 
the instrument will respond. Although all the strings are free to 
vibrate, only those will respond which have the same number of vibra- 
tions per second as the note you sing. Vibrations caused in this way 
are called sympathetic vibrations. 

Echo. — Now, if the same sound is produced, but instead 
of being returned to us by some sympathetic body is of 
sufficient intensity to strike some distant chff or wall, the 
note itself may be returned to us. This returned sound is 
an echo. The formation of an echo is easily understood by 
considering that an elastic medium is similar to an elastic 
ball, and that when it is struck against an obstacle it 
bounds back. 




Sound. 167 

In Fig. 134, if the line AB represents some distant ob- 
stacle, as a building or cliff, and ED the direction of sound 
waves striking it, a person at E would 
hear the sound and shortly afterward ^ 
he would hear the echo. If, however, 
CD represents the direction of the 
sound waves, a person at C would hear / 

no echo because the sound would be ^. 

turned in the direction DF, and a per- F1G.I34. 

son at F would hear the echo. Let 

ED be perpendicular to AB \ then the angle EDC is called 
the angle of incidence, and angle EDF the angle of reflec- 
tion. It has been proved by many experiments that these 
angles are always equal, whatever the direction of the sound 
or the object it strikes. At very short distances echoes 
cannot be distinguished because of the rate at which sound 
travels. 

If a person could say five syllables per second, no echoes 
could be distinct unless the distance were more than 109 
feet. Why .? 

Characteristics of Sound. — Sounds are distinguished 
from each other by intensity, pitch, and quality. 

Intensity. — By the intensity or force of a sound we re- 
fer to the energy with which the sounding body vibrates 
or with which the propagated wave strikes the ear. In- 
tensity depends upon the amplitude of the vibrations of 
the sounding body ; i,e, the greater the amplitude, the more 
intense the sound. If we double the amplitude of a vibra- 
tion, its velocity through a wave length is doubled, and its 
energy becomes four times as great. Hence, (i) the in- 
tensity of sound varies as the square of the amplitude. 



1 68 Elements of Physics. 

Every one knows that the loudness of a/=^ound diminishes 
as its distance from the ear increases, a. ^. we also know 
that the ear cannot tell when one sound is exactly twice, or 
any number of times, as loud as another. We do know, 
however, that the shells of condensation and rarefaction 
are spheres the areas of whose surfaces are ever increasing, 
and that they have greater masses of the medium to affect 
as they proceed from their source; and that the area of 
the surface of a sphere varies as the square of its radius. 
Hence, (2) the intensity of sotmd varies inversely as the 
square of the distance from its source. 

We have learned (Exp. 97) that the rarer the air, the 
fainter the sound. When on the top of high mountains, 
persons have to exert themselves to be heard distinctly, 
and aeronauts have much difficulty in conversing at very 
high altitudes because of the rare atmosphere, but persons 
working in the pneumatic caissons used in building bridge 
piers say that ordinary conversation is extremely painful 
to the ear. From this we learn (3) that the intensity of 
sound depends upon the density of the medium. 

Pitch. — By pitch we mean the relative acuteness of 
sound determined by the rate of vibration. 

Experiment 112. — Take a tin wheel or sheet of stiff cardboard 
about eight and a half inches in diameter and draw concentric circles 
with their circumferences near the edge of the wheel as in Fig. 135. 
On the inner circumference make 24 holes equally distant apart ; on the 
second 30, and on the third 36, and on the fourth 48. Fasten the 
wheel on a rotator where it can be turned very rapidly ; then take a 
small tube, and while turning the wheel very rapidly blow a steady 
stronor current through one of the rows of holes as the wheel rotates. 




Sound. 169 

As the rate of rotate' increases, the tone gets higher and higher until a 
very shrill note is pro -iuced, and as 
the speed slackens the tone grad- 
ually lowers until only a series of 
puffs is heard. 

If such a wheel cannot be had, 
a long comb and a visiting card 
will do. By slowly snapping the 
card over the teeth of the comb, 
and then very rapidly, it will give 
the same result as the wheel. The 

gearing of an old clock will do the 

• r 1 • 1 Fig. 135. 

same if the escapement is removed 

and a card held on one of the turning wheels ; or a card may be 

rubbed against the milled edge of a coin. 

These vibrations show that pitch varies with the rate of 
vibration. The rate of vibration depends upon several 
things. Every one knows that a small string on any in- 
strument gives a higher tone than a large, heavy string, 
and that the same string gives a higher tone when its 
tension is increased or when the length is shortened. 

The number of vibrations required to produce any tone 
may be found by means of an instrument called a vi- 
brograph. 

Experiment 113. — Take a tuning fork, e.g. 3, " C" natural, and to 
one prong fasten a small elastic wire or indicator that may touch the 
surface of a smoked glass plate. Above the glass suspend a pendulum 
with a heavy bob whose time of vibration is exactly known. Fasten to 
the bob a bristle that will just graze the glass as the pendulum swings. 
Now set the fork and pendulum to vibrating at right angles to each 
other, and move the glass plate under them lengthwise to the fork. If 



170 Elements of Physics. 

the pendulum beats seconds, the number of curves the fork makes in 
crossing one of the spaces between two of the transverse lines is the 
number of vibrations the fork makes per second. 

The Diatonic Scale. — By means of this experiment and 
others it has been shown that the vibrations per second 
of a *' C '' fork natural, number 264, and that a sound an 
octave higher than a given sound is produced by twice 
as many vibrations per second. Between two such sounds 
there is a definite number of steps, called musical intervals, 
over which the voice glides in a very pleasing manner. 
These definite musical intervals give rise to the so-called 
diatonic scale ^ the vibration rates of which are as follows : 
^^C" 264, "D" 297, ^^E" 330, ^^F" 352, ^^G" 396, ''A" 
440, *' B " 495, '' C " 528. This scale is the only one which 
gives perfect harmony of chords, and from it many differ- 
ent combinations are made, producing as many different 
tunes. The number of combinations is wonderfully in- 
creased by a scale made from the natural by the use of 
sharps and flats. All musical instruments are made up of 
several octaves, the highest tone of any octave being the 
lowest tone of the next higher, and vice versa. 

Simple and Compound Tones. — Though the natural scale 

is always the same, the number of vibrations producing it 

often differs, depending upon whether the body vibrating 

gives a simple or compound tone. A simple to7ie is one 

made by a body vibrating as a whole, 

,^^^^^^^^^^ and is defined as the lowest tone the 

body can o^ive — it is the fundamental 
Fig. 136. ^ ^ 

tone of that body. A string giving its 
fundamental note has the appearance of a single spindle 
{E, Fig. 136). 



Sound. 



171 



Take a steel wire about 6 feet long, and stretch 



Experiment 114. 
it over a long table as in Fig. 137. Set it to vibrating by drawing a 




Fig. 137. 

bow across its middle, and observe its tone — its fundamental. Mark 

the table so that you can divide the string into fourths, then draw the 

bow across one of these marked points near the end, compare the tone 

with the fundamental, /> 

and observe carefully the ^*C^__.Z^^^^^^C^___I^>'^C^___Z^^^**^CI^ 

form the string assumes Fig. 138. 

when vibrating thus. It will be found that the tone is a little higher 

than the fundamental, and that the form of the string is like AB 

(Fig. 138). 

If we place a bridge at C and draw the bow at D^ as before, the same 
tone will be produced by AC that was produced without the bridge. 

Such a tone produced by a string vibrating in parts 
when no bridge divides it is called an overtone. Now we 
know that the tone of the segment AC is higher than the 
fundamental, and that when they are sounded together 
the segment tends to hasten the fundamental vibrations, 
and that the fundamental tends to retard the vibrations 
of the segment; thereby producing an average or inter- 
mediate tone a little higher than the fundamental. A 
tone thus produced by the harmonious blending of over- 



172 Elements of Physics. 

tones and fundamentals may be called a compound tone. 
In this way tones of different vibration rates are made to 
produce the same pitch. The character of a tone due to 
the harmonious blending of overtones and fundamentals is 
called quality. The degree or fineness of quality depends 
upon the number of overtones blending with the funda- 
mental. 

Musical Instruments. — Considering the character of the 
sound-producing body, musical instruments may be divided 
into three classes: (i) stringed instruments; (2) wind in- 
struments, in which a column of air vibrates ; and (3) plate 
instruments. 

Vibrations of Strings. — Experiment 115. — Stretch two or three 
wires or guitar strings over a sounding board as in Fig. 139 or 137. 

Sound them and carefully note 
the pitch, then slip a bridge 
under them so that they will 
Pj^ vibrate in halves. The tone 

will be found to be an octave 
higher and the vibrations twice as fast. If one fourth is vibrated, 
the tone will be two octaves higher than the fundamental, with a rate 
four times as fast. If a third and fifth are vibrated, their rates will be 
three and five times as fast, respectively. 

Hence, ( i ) the number of vibrations of a string per second 
is inversely proportional to its length. 

Experiment 116. —Using the same instrument as in the above ex- 
periment, regulate the tension of the strings by means of spring balances. 
Pull the spring balance on A until it registers 4 lbs. Note very care- 
fully the pitch of the string, then gradually pull on the spring balance 
till it registers 16 lbs. The tone produced will be found to be an 
octave higher and the vibration rate twice as fast. Rep^a^t t^e e^peri- 




Sound. ' 173 

ment on the other strings with the spring balance registering 9 and 36 
lbs. ; 16 and 64 lbs. The vibration rates will be found twice as great, 
and the tone an octave higher each time. 

Hence, (2) the number of vibrations per second of a string 
varies as the square root of the tension. 

Experiment 117. — Stretch over the sounding board three strings, 
A^ Bj and C, such that the diameter of B is twice that of A, and that 
of C three times that of A. Give A 4 lbs. tension and give B and C 
such tensions as will make them sound in unison with A. Compare the 
tensions, and it will be found that B has 16 lbs. and C 36 lbs. 

Hence, (3) the number of vibrations per second of a string 
varies inversely as the diameter. 

Wind Instruments. — In wind instruments the column of 
air that vibrates is confined within a tube, or a pipe, or 
something that serves the same purpose. In a large 
church organ the air, forced into each pipe by a bellows, 
is driven against the sharp edge of an opening and set to 
vibrating. It then transfers its vibrations to the column 
of confined air. This is seen to be true from the study of 
an ordinary hickory whistle. Every boy knows that the 
longer and larger the body of air inclosed, the louder the 
tone of his whistle. In a French harp, cabinet organ, 
clarinet, and the like, the air is set in motion by the vibra- 
tion of flexible strips of metal or other material called reeds. 
Boys often amuse themselves by cutting along the closed 
end of a goose quill so as to make it whistle when they blow 
into it. 

Experiment 118. — Blow into a glass tube, about one fourth of an 
inch in diameter and five inches long, as you would into a bottle. 
Observe the tone carefully, then place your finger over one end and 



174 Elements of Physics. 

blow again. Compare this tone with the first. It will be found to be- 
an octave lower. Take another tube just half as long as the first and 
compare the tones of both first closed and then open. It will be found 
that the tone of the short one is an octave higher than that of the long 
one. Now compare the tones of the long one open and the short one 
closed, and vice versa. They have the same pitch. 

Hence, in respect to both open and closed pipes the num- 
ber of vibrations is inversely proportional to the length of the 
pipe ; and a7i open pipe gives a to7ie an octave higher than a 
closed pipe of tJie same length. At the end where the wind 
enters, which is always open, there is an antinode, whether 
the pipe is an open or a closed one. If a closed pipe is 
used, there is a node at the closed end, and the inclosed air 
vibrates in a half wave length. If the pipe is open, there 
is a node at the middle and an antinode at each end, caus- 
ing the air to vibrate in a full wave length, hence the 
higher note of an open pipe. 

The Human Voice. — One of the most wonderful reed 
instruments in the world is that by which the human voice 

Glottis Narrow, High Note. Glottis Wider, Quiet Breathing. 

Fig. 140. 

is produced. It is to be admired for its marvelous capabili- 
ties and the extreme simplicity of its parts. This appara- 
tus is situated at the top of the trachea — its location being 




Sound. 



^75 



marked by the ** Adam's apple." Fig. 140 shows the 
organ as seen from above by the use of the laryngoscope. 
C^ is a slit through which the air passes to and from the 
lungs. A and A are thin projecting membranes called the 
vocal cords. In breathing they are loose and lie close to 
the sides of the larynx, but when we wish to speak or sing, 
muscular action takes place and they are brought close 
together so that the air from the lungs, when forced against 
them, sets them to vibrating very much like the tongue of 
a toy trumpet. 

The pitch of the voice varies with the muscular tension 
of the cords, while the intensity depends upon the force 
of the air and the position of the throat and mouth. The 
mouth, throat, and nose form a sort of compound resonance 
box which, by automatic change of form and size, reenf orces 
the action of the cords. For a more careful study of this 
see any good physiology. 

Vibrating Plate Instruments. — Under this head might be 
placed bells, cymbals, tamborines, drums, xylophones, and 
many other instru- 
ments in which 
vibrators are sup- 
ported at their 
nodes and oper- 
ated by soft ham- 
mers, etc. The 
manner in which 
most plates vi- 
brate is shown by 
the following in- 
teresting experi- 
ment : — 




Fig. 141. 



176 



Elements of Physics. 



Experiment i 19. — Fasten any elastic plate, one of brass, for instance, 
as in Fig. 141, and sprinkle fine sand evenly over it, then draw a well- 
resined bow across its edge. A musical note will be produced and the 
sand will at first dance violently around, but will soon come to rest in 
narrow and definitely shaped windrows running in definite directions 
over the plate. These are called nodes, and the parts of greatest vibra- 
tion are called anii nodes. By 
varying the position of the bow 
and touching the plate lightly 
with the finger at the same time 
many different forms may be pro- 
duced (Fig. 142). Wherever the 
plate is touched a node is formed 
and the whole plate divides itself into segments conforming to the 
node thus formed. The sand is always thrown away from the crests 
and collects along the troughs, forming nodal lines. 





Fig. 142. 



Sound Retainers and Reproducers. — Every one knows 
that a child in order to learn to talk must first have the 
sounds impressed upon his organs of hearing and then by 
these organs upon his mental being. In order that this 
might be accomplished the Great Architect planned the 
first sound retainer — the human ear. The sound waves 
enter the outer ear as an ocean wave enters a bay, and 
being reflected inward, strike against the tympanum. Here 
the waves produce a plate vibration which is transmitted to 
the inner ear, or cochlea. To the eardrum are attached 
three little bones — anvil, hammer, stirrup — which serve 
as a medium to transmit the waves to the cochlea. The 
cochlea is filled with a liquid in which are stretched many 
filaments of the auditory nerve. The foot plate of the 
stirrup connects directly with the cochlea so that sound 



Sound. 



177 



vibrations striking the ear drum are transmitted to the 
cochlea, and being taken up by these filaments, produce 
the sensation of hearing. This arrangement is sometimes 
likened to a harp of 3000 strings, there being about that 
number of filaments. These filaments, whose vibration 
periods correspond with the external sound waves, are 



Semicircular Canals '>s 



"^■""rrup Anvil 




Fig. 143. 



thrown into sympathetic vibration. The trembling of 
these nerve filaments is transmitted to the auditory nerve, 
and thence to the brain, where the impressions are received. 
When the number of vibrations is less than 16 per second 
or more than 38,000 per second, the sound is not percep- 
tible by the human ear. 

The Phonograph. — The phonograph is an instrument 
for the retention of and reproduction of sound. It acts 
upon the principle that vibrations of a given intensity, rate, 
and form always produce the same sound. The instru- 



178 Elements of Physics. 

ment has a vibrating membrane or plate, corresponding to 
the ear drum, to the middle of which is fastened a very- 
hard point, or stylus, corresponding to the hammer of the 
ear. The whole acts very much as the ear does. A large 
funnel corresponding to the auditory canal collects the 
sound waves so that they strike against the vibrating plate. 
Corresponding to the brain is a receiver made of wax 
having a smooth surface over which the stylus is made to 
move so as to barely touch. When a sound is sent into 
the funnel, it causes the drum plate to vibrate in unison, so 
that the stylus plows a little furrow in the wax and makes 
a series of successive dots and dashes along the bottom 
of the furrow, corresponding to every pulse of the sound 
wave — the depth depending upon the intensity of the 
sound and the number in any given distance depending 
upon the pitch. 

After the impression is made upon the wax surface the 
stylus is started at the beginning of the furrow and allowed 
to retrace. It will, in going over the indentations, cause 
the drum plate to vibrate, as the latter first vibrated the 
stylus, and thus to return through the funnel the vibrations 
that were sent into it at first. In this way, the phono- 
graph reproduces talking, laughing, music, or sounds of 
any kind. By this means many generations from now 
people may hear again the great musicians and orators of 
to-day delivering their parts with the vim and energy of life. 

Questions. — i. Define acoustics. Define sound. 

2. By what is sound produced? 

3. What three vibrations are necessary before the sensation of 
hearing is produced? 



Sound. 179 



4. How do we know that a sounding body vibrates? 

5. Do fish hear? 

6. How may a rotten spot in a wooden beam be detected? 

7. What is a string telephone? 

8. How do we know that sound does not travel through a vacuum? 

9. Find the velocity of sound in the air at 70° F. 

10. Prove that all sounds travel at the same rate. 

11. I hear the thunder 41 seconds after I see the flash of lightning. 
How far away is it? 

12. I see a flash and hear the report of the gun 6 seconds after- 
wards. How far away is the gim? 

13. What is meant by interference of sound? 

14. How can you illustrate interference? 

15. What are beats in sound? How are they produced? 

16. What is meant by reflection of sound? 

17. What are whispering galleries? 

18. On what does the number of syllables repeated by an echo 
depend? 

19. Why is it that persons often hold the hand behind the ear that 
they may hear? 

20. What laws govern the pitch of strings? 

21. What are overtones? 

22. When is a tone reenforced? 

23. When is the reenforcement strongest? 

24. What are elements of sound? On what does each depend? 
How can we prove it ? 



i8o Elements of Physics. 



25. Why does the number of vibrations producing a given sound 
vary ? 

26. Why does the pitch of a pipe rise when the current of air is 
increased? 

27. What is the position of the vocal cords in producing a falsetto 
voice ? 

28. Why is the average woman's voice an octave higher than a 
man's ? 

29. What is speech? 

30. Why does not confusion arise from hearing with two ears? 

31. Why do shells of a certain shape murmur when held to the ear? 

32. Why are musical instruments provided with sounding boards? 

33. Explain the influence of disease, joy, and sorrow upon the vocal 
cords. 

34. Of what is the diatonic scale formed? 

35. What other scales are there, and how are they formed? 



INDEX. 



Absolute zero, 70. 
Acoustics, 157. 
Adhesion, 8. 
Air, liquid, 75. 
Air pump, 44. 
Ampere's law, 133. 
Artificial cold, 74. 

Ice, 75. 
Atom, 3. 

Attraction, laws of magnetic, no. 
Attraction of gravitation, 13, 14. 

Capillary, 10. 

Mass, 13. 

Barometer, 44. 

Uses of, 46. 
Bichromate cell, 126. 
Boiling, 73. 

Point, 74. 
Boyle's law, 43. 
Buoyancy, 52. 

Camera, 105. 
Capillary attraction, 10. 
Centripetal force, 27, 28. 
Charles's law, 70. 
Chemical division, 3. 
Cohesion, 8. 
Color, 96, 105. 
Commutator, electric, 151. 
Component forces, 20. 
Composition of forces and motion, 

21. 
Compressibility, 5. 
Conduction of heat, 59. 

Of electricity, 119. 
Conservation of energy, 58. 



Convection, 61. 
Current induction, 134. 

Daniell cell, 125. 
Diatonic scale, 170. 
Divisibility, 2. 
Limit of, 2. 
Ductility, 10. 
Dynamo, 150. 

Ear, human, 177. 

Echo, 166. 

Elasticity, 4. 

Electric batteries, 125-127. 

Electric currents, effects of, 127. 

Electricity, 116. 

Commercial applications of, 142, 156. 

Positive and negative, 117. 
Electrolysis, 128. 
Electro-magnets, 135. 
Electrophorus, 122. 
Electroplating, 143. 
Electroscope, 121. 
Electrotyping, 142. 
Energy, 29, 31. 

Conservation of, 58. 

Formulas for calculating, 32. 

Kinetic, 30. 

Potential, 30. 

Transformation and indestructibility 
of, 57. 

Units of, 31. 
Engine, steam, 78. 

Gasoline, 79. 

Hot air, 79. 

Naphtha, 80. 
Equilibrant, 21. 

181 



l82 



Index. 



Equilibrium, 24. 

Kinds of, 24, 25. 
Ether, 63. 
Evaporation, 72. 
Expansion, 64. 

Of gases, 69. 
Experiment, 2. 
Eye, human, 104-105. 

Fluids, pressure of, 40. 
Force, 7. 

Attractive, 8. 

Centrifugal, 28. 

Centripetal, 27. 

Composition and resolution of, 20, 21. 

Effect of constant, 17. 

Electro-motive, 140. 

Repellent, 8. 
Formulae, 18, 19, 20, 22, 32, 67, 79, 140, 142. 
Friction, 56. 

Galvanic cell, 123. 

Galvanometer, 129. 

Gases, compressibility of, 42. 

Elasticity of, 42. 

Volume of, 43. 
Gravitation, 13, 23. 

Newton's law of, 14. 
Gravity, centre of, 24. 
Grenet cell, 126. 

Heat, effects of, 64. 

Latent, 71. 

Mechanical applications of, 68, 77. 

Mechanical equivalent of, 56. 

Sources of, 55, 56. 

Specific, 70. 

Theory of, 55. 

Transference of, 59. 
Heliograph, 106. 
Hydrostatic press, 48, 

Impenetrability, 5. 
Inclined plane, 36. 
Indestructibility, 5. 
Induction, 121. 

Coil, 137. 

Current, 134. 

Electro-magnetic, 135. 



Induction — 

Magnetic, in. 
Intensity of sound, laws of, 167. 

Kinetic energy, 30. 

Law of Charles, 70. 

Gravitation, 14. 
Laws of intensity of sound, 167. 

Motion, II, 12, 13, 18, 19. 

Vibration of strings, 172. 
Leclanche battery, 127. 
Lenses, 99. 

Concave, 102. 

Convex, loi. 

Foci of, 100. 
Levers, 33, 34, 35. 
Light, 82. 

Decomposition of, 95. 

Dispersion of, 95. 

Internal reflection of, 95. 

Nature of, 83. 

Rectilinear motion of, 85. 

Reflection of, 88. 

Synthesis of, 97. 

Velocity of, 85. 
Lighting, electric, 152. 

Incandescent, 153. 
Lightning, 119. 
Lightning rods, 120. 
Liquid air, 75. 
Liquids, pressure of, 40, 49. 

Transmission of pressure, 48. 

Machines, 33. 
Magnetic field, no. 

Needle, 113. 
Magnetism, 109. 

Nature of, in. 
Magnets, 109. 

Care of, no. 

Electro-, 135. 
Malleability, 10. 
Mass, 4. 

Attraction of, 13. 

Center of, 24. 
Matter, i. 

Properties of, 4, 5, 10. 

Theory of the constitution of, 3. 



Index. 



183 



Melting point, 71. 
Microscope, 102. 
Mirrors, plane, 89. 

Concave, 90. 

Convex, 92. 
Molecule, 3. 
Momentum, 11, 22. 

Change of, 16, 22. 
Motion, 6. 

Composition and resolution of, 21, 
22. 

Curvilinear, 7, 26. 

Kinds of, 7. 

Laws of, II, 12, 13. 

Rotary, 7. 

Translatory, 7. 

Uniformly accelerated, 15, 17, 18, 19. 

Vibratory, 7. 
Motor, electric, 149. 
Musical instruments, 172. 

Needle, magnetic, 113. 

Declination of, 113. 

Inclination of, 114. 
Newton's laws of motion, 11, 12, 13. 

Law of gravitation, 14. 

Ohm, 138. 
Ohm's law, 140. 

Application of, 141. 

Pendulum, 25, 26. 
Phonograph, 177. 
Photometry, 83. 
Physical division, 3. 
Polarization of batteries, 124. 
Porosity, 4. 
Potential energy, 30. 
Pressure of fluids, 40. 
Prisms, 95. 

Problems, 20, 23, 32, 39. 
Pulleys, 35, 36. 
Pump, air, 44. 

Condenser, 46. 

Force, 47. 

Lifting, 47. 

Questions, i, 25, 28, 31, 38, 45, 51, 60, 80, 
93, 106, 115, 155, 178. 



Radiation, 62. 
Radiometer, 63. 
Reflection of light, 88. 

Internal, 95. 
Refraction, 92. 

Angle of, 93. 

Index of, 93. 
Resistance, laws of electrical, 139. 
Resolution of forces and motion, 20, 21. 
Resonance, 165. 
Resonator, 166. 
Resultant, 20. 
Ruhmkorff coil, 154. 

Scale, diatonic, 170. 
Screw, 37. 
Shadows, 86. 
Siphon, 50. 
Solenoid, 132. 
Sound, 157. 

Beats, 164. 

Intensity, 167. 

Interference, 163. 

Pitch, 168. 

Retainers and reproducers, 176. 

Sources of, 158. 

Transmission of, 158. 

Velocity of, 161. 

Vibrations of, 157. 

Waves, 162. 
Specific gravity, 53. 
Specific heat, 70. 
Spectroscope, 97. 
Spectrum, solar, 96. 
Speech, 17. 
Steam engine, 78. 
Stereopticon, 106. 

Telegraph, electric, 144. 

Multiple, 147. 

Wireless, 146. 
Telephone, 149. 
Telescope, 103. 
Tenacity, 10. 
Thermometers, 66-68. 

Centigrade, 67. 

Fahrenheit, 67. 

Maximum, 67. 

Metal, 68. 



i84 



Index. 



Thermometers — 
Minimum, 67. 
Thermometry, 65. 
Toepler-Holz machine, 122. 
Tones, simple and compound, 170. 
Torricellian vacuum, 45. 
Transformer, electrical, 154. 

Vacuum, 45. 
Velocity, 17. 

Of light, 85. 

Of sound, 161. 
Ventilation, 61. 



Vibrations of sound, 157. 

Of strings, 172. 
Visual angle, 87. 
Voice, human, 174. 
Voltaic cell, 123. 
Volume, 4. 

Wedge, 37. 

Wheatstone's bridge, 139. 
Wheel and axle, 34. 
Wind instruments, 173. 
Work, 29, 30. 
Units of, 31. 



- i<iaa 



.rjO? 



^ COPY Oa.VO CAT. DW. 
MAY 5 1902 



LIBRARY OF CONGRESS 





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003 647 373 3 • 


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